hyph-an-counts(1).txt

monoidal category: 93
double category: 71
topological space: 45
small category: 43
distributive law: 37
abelian category: 36
symmetric monoidal category: 33
symmetric monoidal: 31
weak equivalence: 31
differential category: 27
right adjoint: 26
crossed module: 26
simplicial set: 26
natural transformation: 25
categorical group: 25
universal property: 24
special case: 23
monoidal structure: 22
full subcategory: 21
semi - abelian category: 21
main result: 20
abelian group: 19
monoidal bicategory: 19
universal algebra: 18
sufficient condition: 17
presentable category: 17
algebraic theory: 17
categorical structure: 17
internal category: 17
cartesian differential category: 17
geometric morphism: 16
complete category: 16
metric space: 16
protomodular category: 15
finite product: 15
algebraic structure: 14
effective descent morphism: 14
left adjoint: 14
differential geometry: 14
finite limit: 14
exact category: 13
regular epimorphism: 13
such category: 13
closed category: 13
exact completion: 13
regular category: 13
exact sequence: 12
autonomous category: 12
internal groupoid: 12
linear logic: 11
commutative ring: 11
cubical set: 10
general result: 10
monoidal functor: 10
extensive category: 10
virtual double category: 9
lax functor: 9
central extension: 9
presheaf category: 9
algebraic geometry: 9
several example: 9
light factorization: 9
monoidal model category: 9
finite group: 8
full subcategorie: 8
previous work: 8
finite set: 8
accessible category: 8
continuous map: 8
explicit construction: 8
main theorem: 8
present paper: 8
homological category: 8
enriched category: 8
fibrant object: 7
reflective subcategory: 7
necessary condition: 7
principal bundle: 7
boolean algebra: 7
finite coproduct: 7
projective object: 7
discrete fibration: 7
general theory: 7
boolean flow: 7
general notion: 7
other hand: 7
new notion: 7
exactness condition: 7
inverse semigroup: 7
smooth map: 7
quantum category: 7
quillen equivalence: 6
additive category: 6
homological algebra: 6
free algebra: 6
certain condition: 6
general category: 6
distributive category: 6
continuous function: 6
terminal object: 6
first step: 6
algebraic topology: 6
maltsev category: 6
analogous result: 6
such functor: 6
dimensional structure: 6
new example: 6
previous paper: 6
geometrical category: 6
lax extension: 6
subtractive category: 6
strict omega: 6
combinatorial model category: 6
coherent unit action: 6
symmetric monoidal bicategory: 6
small quantaloid: 6
representable functor: 6
forgetful functor: 6
first author: 6
partial map category: 6
idempotent pseudomonad: 6
polynomial monad: 6
weak model category: 6
smooth manifold: 5
elementary topos: 5
lax morphism: 5
synthetic differential geometry: 5
strong monoidal functor: 5
additional structure: 5
large class: 5
present article: 5
natural example: 5
categorical trace: 5
normal subobject: 5
presheaf topos: 5
precubical set: 5
open set: 5
normal monomorphism: 5
general context: 5
free cocompletion: 5
categorical model: 5
associative algebra: 5
linear functor: 5
concrete geometrical category: 5
other work: 5
fundamental groupoid: 5
cartesian closed category: 5
distributive lattice: 5
cokleisli category: 5
opmonoidal monad: 5
independent interest: 5
faithful functor: 5
bisimplicial set: 5
injective hull: 5
complicial set: 5
categorical action: 5
spectral space: 5
universe category: 5
hypergraph category: 5
special commutative: 5
spectral vector bundle: 5
split extension: 5
strict monoidal: 5
noetherian form: 5
internal equivalence relation: 4
partial order: 4
basic theory: 4
boolean category: 4
recent work: 4
exact functor: 4
weak factorization system: 4
new characterization: 4
simplicial group: 4
new one: 4
differential form: 4
different notion: 4
fundamental group: 4
appropriate notion: 4
suitable category: 4
exact protomodular category: 4
important example: 4
multiplicative linear logic: 4
natural number: 4
new approach: 4
compact space: 4
dimensional analogue: 4
lax epimorphism: 4
equational hull: 4
suitable sense: 4
natural generalization: 4
internal structure: 4
weak notion: 4
dynamical system: 4
cyclic spectrum: 4
real number: 4
geometric logic: 4
exponential principle: 4
various example: 4
dimensional category: 4
cubical nerve: 4
high category theory: 4
categorical property: 4
categorical semantic: 4
simplicial object: 4
reflexive graph: 4
coreflective subcategory: 4
new way: 4
harmonic oscillator: 4
categorical crossed module: 4
special attention: 4
unary operation: 4
explicit description: 4
subtractive variety: 4
exponentiable object: 4
closed bicategorie: 4
weak double category: 4
direct sum: 4
lax algebra: 4
arbitrary morphism: 4
other approach: 4
linear category: 4
normal category: 4
arbitrary category: 4
projective model structure: 4
high dimensional transition system: 4
dimensional transition system: 4
adhesive category: 4
first part: 4
axiomatic framework: 4
weak wreath product: 4
complicial identity: 4
direct proof: 4
codensity monad: 4
dimensional vector space: 4
early work: 4
finite colimit: 4
monoidal differential category: 4
cartesian closed: 4
exact homological category: 4
permutable category: 4
isotropy group: 4
inductive groupoid: 4
electrical circuit: 4
symmetric strict monoidal: 4
free double category: 3
own right: 3
double lie: 3
rinehart structure: 3
monoidal abelian category: 3
stable unit: 3
small object: 3
horizontal unit: 3
horizontal morphism: 3
categorical framework: 3
deductive system: 3
pointed object: 3
common generalization: 3
topological quantum field theory: 3
abelian object: 3
certain category: 3
full reflective subcategory: 3
simple description: 3
simple proof: 3
algebraic model: 3
new construction: 3
multipresentable category: 3
original category: 3
free category: 3
abstract characterization: 3
strict algebra: 3
compatible structure: 3
thin structure: 3
finitary monad: 3
natural number object: 3
equational category: 3
discrete object: 3
finite graph: 3
extra structure: 3
dual quasi - bialgebra: 3
symmetric cat: 3
categorical sense: 3
new proof: 3
conceptual proof: 3
different category: 3
concrete functor: 3
high dimensional automata: 3
dimensional automata: 3
thin element: 3
finite ordinal: 3
classical property: 3
complete spread: 3
many generator: 3
special kind: 3
such notion: 3
cocomplete category: 3
new type: 3
set theory: 3
cyclic flow: 3
fundamental category: 3
projective module: 3
double groupoid: 3
recognizable forest: 3
algebraic lattice: 3
normal epimorphism: 3
globular nerve: 3
equivariant stable homotopy theory: 3
stable homotopy theory: 3
particular case: 3
linear bicategory: 3
linear setting: 3
weak inverse: 3
presentable morphism: 3
presentable object: 3
regular epi: 3
monoidal object: 3
different context: 3
terminal coalgebra: 3
iterative algebra: 3
such monad: 3
equivalent condition: 3
suitable subcategory: 3
global section: 3
free restriction category: 3
unital category: 3
important result: 3
same object: 3
open problem: 3
categorical approach: 3
topological cospan: 3
classical theorem: 3
quillen equivalent: 3
free object: 3
cartesian bicategory: 3
framed bicategory: 3
categorical analogue: 3
algebraic category: 3
full embedding: 3
initial object: 3
autonomous structure: 3
connected case: 3
new class: 3
different construction: 3
canonical way: 3
globular complex: 3
early paper: 3
weak distributive law: 3
geometric realization: 3
additional condition: 3
categorical algebra: 3
symmetric multicategorie: 3
globular operad: 3
standard construction: 3
dual equivalence: 3
vertical arrow: 3
stochastic automata: 3
usual tensor product: 3
partial map: 3
topological group: 3
special class: 3
coreflective subcategorie: 3
coherent category: 3
vertical morphism: 3
generalized notion: 3
lefschetz number: 3
algebraic description: 3
inverse category: 3
categorical context: 3
commutative square: 3
ary site: 3
strong relation: 3
strict unit: 3
parallel transport: 3
certain property: 3
compact closed: 3
quillen model category: 3
monetary value measure: 3
topological functor: 3
universal object: 3
like structure: 3
theoretic term: 3
magnetic monopole: 3
universe category functor: 3
last section: 3
linear relation: 3
pointed exact protomodular category: 3
compact regular frame: 3
regular frame: 3
symmetric quandle: 3
lax monoidal functor: 3
tangent category: 3
effective category: 3
weak cofibration category: 3
cofree cartesian differential category: 3
symmetric sequence: 3
opmonoidal arrow: 3
black box functor: 3
lax pullback complement: 3
canonical triangulation: 3
double category construction: 3
complete metric space: 3
equivariant operad: 3
monic skeleta: 3
extranatural transformation: 3
multiplicative vector field: 3
other colimit: 3
extriangulated category: 3
canonical isomorphism: 2
general setting: 2
particular example: 2
arithmetic universe: 2
commutative monoidal category: 2
well understanding: 2
preadditive category: 2
systematic construction: 2
symmetric monoidal abelian category: 2
light factorization system: 2
horizontal target: 2
augmented virtual double category: 2
reflective subfibration: 2
topological complexity: 2
intuitionistic logic: 2
right exact functor: 2
comma category: 2
strong one: 2
subcanonical site: 2
free completion: 2
semistrict monoidal: 2
usual axiom: 2
coherent isomorphism: 2
continuous flow: 2
weak dihomotopy equivalence: 2
affine category: 2
full structure: 2
full sub: 2
pointed space: 2
different class: 2
crossed square: 2
commutative algebra: 2
useful property: 2
trivial covering: 2
local homeomorphism: 2
stable homotopy category: 2
strong promonoidal functor: 2
quantic conuclei: 2
complete characterization: 2
denotational semantic: 2
new model: 2
suitable generalization: 2
singular chain complex: 2
idempotent monad: 2
left exact: 2
explicit calculation: 2
discrete group: 2
logical axiom: 2
operad action: 2
lax equivalent: 2
familiar term: 2
categorical theory: 2
finite sum: 2
suitable factorization system: 2
simple characterization: 2
flat functor: 2
simplicial version: 2
universal coefficient: 2
exponentiable space: 2
ultrafilter monad: 2
strict natural transformation: 2
lax monad: 2
symmetric double category: 2
discrete opfibration: 2
formal property: 2
non - commutative negation: 2
free multiplicative linear logic: 2
regular extension: 2
local presentability: 2
regular cardinal: 2
contravariant functor: 2
certain kind: 2
open subset: 2
natural definition: 2
discrete space: 2
open map: 2
contravariant powerset functor: 2
simplicial groupoid: 2
pointed case: 2
differential equation: 2
strange attractor: 2
varietal case: 2
epireflective subcategorie: 2
integral domain: 2
surjective homomorphism: 2
modular variety: 2
small class: 2
ordinary category: 2
balanced coalgebroid: 2
balanced monoidal category: 2
quasi - triangular dual quasi - bialgebra: 2
surjective functor: 2
relational sum: 2
proper subcategory: 2
small coproduct: 2
new result: 2
universal functor: 2
absolute colimit: 2
topological hull: 2
internal characterization: 2
categorical proof: 2
basic category: 2
small colimit: 2
reduced branching homology: 2
topological abelian group: 2
relevant category: 2
symmetric simplicial set: 2
classical one: 2
globular cardinal: 2
globular set: 2
explicit formulae: 2
sifted colimit: 2
reflexive coequalizer: 2
explicit characterization: 2
classical result: 2
free group: 2
homotopical exactness: 2
certain object: 2
unified proof: 2
first model: 2
certain equaliser: 2
compact locale: 2
certain quotient: 2
new definition: 2
pure subobject: 2
geometric theory: 2
pure morphism: 2
flat module: 2
sided enrichment: 2
natural isomorphism: 2
arbitrary base category: 2
internal locale: 2
lextensive category: 2
certain monad: 2
high dimensional structure: 2
usual notion: 2
lax natural transformation: 2
pointed endofunctor: 2
various notion: 2
partial topos: 2
local topos: 2
compact support: 2
algebraic context: 2
cubical site: 2
ary term: 2
binary term: 2
strict globular: 2
simplicial nerve: 2
semi - cubical nerve: 2
such result: 2
essential point: 2
ordinary bicategorie: 2
linear bicategorie: 2
lax transformation: 2
dimensional generalization: 2
3rd cohomology class: 2
strict lie: 2
various result: 2
reflective subcategorie: 2
relevant example: 2
strict version: 2
fold monoidal: 2
categorical version: 2
generalized operad: 2
opetopic approach: 2
high dimensional category theory: 2
dimensional category theory: 2
universal construction: 2
idempotent splitting completion: 2
normed cubical set: 2
arbitrary variety: 2
small set: 2
flat weight: 2
legitimate category: 2
semi - direct product: 2
direct product: 2
semi - abelian variety: 2
abelian variety: 2
binary coproduct: 2
precise form: 2
commutative quantale: 2
suitable hypothesis: 2
commutative cube: 2
cartesian monad: 2
planar polycategorie: 2
compact closed category: 2
abstract notion: 2
bipartite projector: 2
key property: 2
strong compact closure: 2
compact closure: 2
commutative shell: 2
appropriate set: 2
strong adjunction: 2
other model: 2
additive functor: 2
epimorphic hull: 2
recent field: 2
quillen model category structure: 2
internal equivalence: 2
semi - abelian: 2
strong equivalence: 2
interesting example: 2
simple condition: 2
combinatorial nature: 2
different approach: 2
classical notion: 2
infinite set: 2
combinatorial specie: 2
quantum mechanic: 2
more structure: 2
connected component: 2
classical case: 2
topological object: 2
indexed category: 2
natural topology: 2
categorical level: 2
dimensional version: 2
pre - numeral: 2
simple example: 2
conformal field theory: 2
similar result: 2
thin filler condition: 2
pure monomorphism: 2
other way: 2
underlying bicategory: 2
various approach: 2
theoretic construction: 2
natural deduction formulation: 2
classical logic: 2
intrinsic multiple conclusion: 2
multiple conclusion: 2
quotient category: 2
collarable cospan: 2
cubical cospan: 2
regular operad: 2
linear equation: 2
stable isomorphism: 2
closed surface: 2
similar fashion: 2
extensive quantity: 2
abstract core: 2
binary operation: 2
pseudonatural transformation: 2
recursive equation: 2
unique solution: 2
close connection: 2
multiplicative structure: 2
mathematical structure: 2
bicategorical notion: 2
framed bicategorie: 2
monoidal fibration: 2
symmetric categorical group: 2
general theorem: 2
dual category: 2
zeroary operation: 2
adjunctible map: 2
underlying category: 2
internal set: 2
internal hom: 2
theoretic model: 2
future paper: 2
main purpose: 2
general case: 2
local connectedness: 2
discrete locale: 2
internal approximate: 2
suitable condition: 2
weak preservation: 2
finitary functor: 2
convenient category: 2
main advantage: 2
second author: 2
recent paper: 2
familiar notion: 2
differential operator: 2
basic property: 2
finite derivation type: 2
symbolic dynamic: 2
linear map: 2
mixed distributive law: 2
coherent model: 2
enriched orthogonality: 2
many case: 2
fibred category: 2
absolute cr: 2
epic space: 2
open question: 2
categorical counterpart: 2
subtractive span: 2
weak version: 2
multiplicative graph: 2
semiabelian context: 2
internal crossed module: 2
double central extension: 2
third cohomology group: 2
monadic approach: 2
internal family: 2
final functor: 2
natural generalisation: 2
same time: 2
intrinsic description: 2
unified framework: 2
related structure: 2
generalized multicategorie: 2
linear operator: 2
projective geometry: 2
right action: 2
temporal doctrine: 2
free monoid: 2
strong epimorphism: 2
stratified manifold: 2
transversal homotopy monoid: 2
high invariant: 2
transversal homotopy category: 2
accessible functor: 2
negative integer: 2
quillen model structure: 2
new structure: 2
coherent space: 2
partial operation: 2
closed structure: 2
simplified description: 2
certain double category: 2
covariant presheave: 2
weak high dimensional transition system: 2
cubical transition system: 2
categorified algebra: 2
certain exactness condition: 2
compact quantum group: 2
broad sense: 2
categorical method: 2
weak homotopy equivalence: 2
simple formula: 2
various construction: 2
abstract framework: 2
high category: 2
other kind: 2
certain type: 2
lax version: 2
submultiplicative order: 2
injective object: 2
relative cell complex: 2
algebraic weak factorisation system: 2
weak factorisation system: 2
trivial fibration: 2
classical theory: 2
joint paper: 2
hopf monad: 2
algebraic object: 2
autonomous comonad: 2
further application: 2
dimensional cube: 2
colax idempotent pseudomonad: 2
lax idempotent pseudomonad: 2
elementary quotient completion: 2
useful tool: 2
categorical commutator: 2
semi - abelian context: 2
abelian context: 2
complete morphism: 2
closed map: 2
commutative monoid: 2
uniform structure: 2
high central extension: 2
enough projective: 2
ary exact category: 2
small site: 2
pointed context: 2
regular subtractive category: 2
epimorphic pair: 2
strong monomorphism: 2
exponentiable morphism: 2
difunctional relation: 2
commutative semigroup: 2
constant object: 2
applicative morphism: 2
ergodic action: 2
homogeneous space: 2
supercommutative algebra: 2
central importance: 2
weakly globular double category: 2
globular double category: 2
particular class: 2
lax monoidal structure: 2
principal result: 2
subsequent work: 2
funny tensor product: 2
tight span: 2
semi - tropical module structure: 2
tropical module structure: 2
open topological groupoid: 2
topological groupoid: 2
equivariant sheaf: 2
smoothness condition: 2
nontrivial reflective subcategory: 2
clean ring: 2
corresponding algebra: 2
bisimplicial presheave: 2
diagonal functor: 2
such morphism: 2
distributive space: 2
partial combinatory algebra: 2
bicategorical localization: 2
idempotent core: 2
local equivalence: 2
generalized model category: 2
cohesive geometric morphism: 2
weak form: 2
simplicial model category: 2
simple functor: 2
relative category: 2
present work: 2
other category: 2
conditional expectation: 2
dynamic monetary value measure: 2
relative entropy: 2
cartesian lifting: 2
technical result: 2
weighted colimit: 2
concrete example: 2
rational function: 2
theoretic context: 2
pointed category: 2
balanced effective descent morphism: 2
quasi spectral space: 2
previous construction: 2
various kind: 2
extra assumption: 2
categorical polynomial monad: 2
total category: 2
operad module: 2
several entry: 2
local symmetry: 2
triple category: 2
dimensional cell: 2
interchange law: 2
coreflective hull: 2
final object: 2
trivial cofibration: 2
topological group structure: 2
duplicial object: 2
categorical perspective: 2
arbitrary lie groupoid: 2
finite category: 2
second cohomology categorical group: 2
cocomplete linear category: 2
unbiased contraction: 2
several reformulation: 2
formal theory: 2
complete distributivity: 2
complete partial order: 2
simplified model: 2
high categorical structure: 2
double functor: 2
quasi - schemoid: 2
careful proof: 2
localic groupoid: 2
diffeological space: 2
compact closed bicategorie: 2
weak pullback: 2
gerbal representation: 2
quotient vector bundle: 2
topological vector space: 2
additional model category structure: 2
original one: 2
relative point: 2
nilpotent object: 2
relative internal action: 2
internal action: 2
categorical principal bundle: 2
geometric context: 2
abelian symmetric quandle: 2
coherent site: 2
equational theory: 2
regular image: 2
short map: 2
approximate categorical structure: 2
particular interest: 2
monoidal pseudofunctor: 2
simplicial lie algebra: 2
hypercrossed complex: 2
same result: 2
complete lattice: 2
explicit model: 2
symmetric lax monoidal functor: 2
chemical reaction network: 2
skeletal cancellative: 2
regular functor: 2
constructive proof: 2
semi - simple algebra: 2
simple algebra: 2
other word: 2
cyclic operad: 2
tangent bundle: 2
axiomatic definition: 2
monic span: 2
general condition: 2
tame polynomial: 2
binary product structure: 2
cancellative small category: 2
steady state: 2
atomic geometric morphism: 2
crossed product: 2
strict symmetric monoidal category: 2
new crossed module: 2
differential bundle: 2
equivalent formulation: 2
complete inductive groupoid: 2
external behavior: 2
lagrangian linear relation: 2
good atlas: 2
dimensional sphere: 2
parallel section: 2
split cube: 2
isotropy rank: 2
formal approach: 2
stable derivator: 2
monotone continuous map: 2
lax limit: 2
weak duality involution: 2
reflexive space: 2
symmetric operad: 2
monoidal version: 2
joyal model structure: 2
simple criterion: 2
weak analogue: 2
degenerate boundary: 2
representable merge: 2
operadic nerve: 2
genuine equivariant operad: 2
skeletal boundary: 2
invariant multiplicative vector field: 2
sufficient criterion: 2
closed subcategory: 2
reversed span: 2
relative nerve: 2
oidal monad: 2
maximal rigid subcategorie: 2
rigid subcategorie: 2
involutive analog: 2
colored operad: 2
restricted diagram: 2
cohesive topos: 2
quadratic algorithm: 1
special functor: 1
cube category: 1
non - canonical isomorphism: 1
non - canonical decomposition: 1
canonical decomposition: 1
triple vector bundle: 1
modular tensor category: 1
spherical fusion category: 1
isomorphic orbifold: 1
representable definition: 1
main aim: 1
natural model category: 1
strict symmetric monoidal: 1
numerous result: 1
combinatorial model category structure: 1
corresponding infinity: 1
equivariant coarse algebraic: 1
equivariant version: 1
convenient way: 1
many infinity: 1
internal preorder: 1
internal partial order: 1
stable regular epimorphism: 1
admissible categorical: 1
topological interpretation: 1
latter category: 1
horizontal multi: 1
single horizontal target: 1
latter notion: 1
empty horizontal target: 1
formal category: 1
admissible object: 1
virtual double category coincide: 1
double category coincide: 1
classical composition: 1
new homology: 1
archimedean place: 1
singular homology: 1
real coefficient: 1
equivalent necessary condition: 1
homological dimension: 1
small cancellative category: 1
cancellative category: 1
homological dimension one: 1
binary product: 1
partial morphism category: 1
productive terminal: 1
valuable tool: 1
real world datum: 1
several approach: 1
arbitrary set: 1
combinatorial persistence: 1
common categorical framework: 1
novel framework: 1
classical equality: 1
many category: 1
colorable rank: 1
semisimple abelian category: 1
persistent homology: 1
local map: 1
equivariant principal bundle: 1
invariant topological complexity: 1
abstract algebraic structure: 1
same sense: 1
canonical axiomatisation: 1
possible such axiomatisation: 1
such axiomatisation: 1
medial map: 1
free deductive system: 1
boolean logic: 1
single free algebra: 1
empty set: 1
decidable topos: 1
natural common generalization: 1
slanted product: 1
other hand subcanonical: 1
simultaneous left: 1
powerful result: 1
nice feature: 1
full dihomotopy relation: 1
pointed protomodular category: 1
internal construction: 1
specific characterization: 1
generalized congruence: 1
concrete construction: 1
various other class: 1
other class: 1
epimorphic functor: 1
distinct enrichment: 1
many monoidal structure: 1
unique isomorphism: 1
such distinction: 1
precise mathematical definition: 1
mathematical definition: 1
restricted class: 1
idempotent dual: 1
stable local coequalizer: 1
local coequalizer: 1
familiar bimodule: 1
general module: 1
idempotent relation: 1
semi - group: 1
different closed model category structure: 1
closed model category structure: 1
same class: 1
other structure: 1
neat description: 1
inverse functor: 1
precise characterization: 1
other sketch: 1
strong colimit: 1
limited completeness: 1
precise statement: 1
many practical example: 1
practical example: 1
absolute notion: 1
general relative: 1
many question: 1
disparate condition: 1
old result: 1
quintessential localization: 1
idempotent natural endomorphism: 1
natural endomorphism: 1
persistent localization: 1
boolean topos: 1
basic fact: 1
combinatorial groupoid theory: 1
characteristic class: 1
first neighbourhood: 1
basic combinatorial structure: 1
combinatorial structure: 1
fundamental crossed module: 1
complex method: 1
classical infinite loopspace machine: 1
connective spectra: 1
existential quantification: 1
free monoidal category: 1
promonoidal category: 1
like transform: 1
cartesian product: 1
orthomudular lattice: 1
associative disjunction operation: 1
prime characteristic: 1
modified version: 1
particular kind: 1
interesting result: 1
medial rule: 1
classical propositional logic: 1
propositional logic: 1
double order structure: 1
large rectangle: 1
such tiling: 1
forbidden suborder: 1
planar graph: 1
ordinary singular chain complex: 1
new version: 1
more algebraic structure: 1
pointed set: 1
adequate algebraic model: 1
free regular: 1
various rank: 1
weak limit: 1
standard technique: 1
classical glueing theorem: 1
open subtopos: 1
closed complement: 1
simple form: 1
important property: 1
partial algebra: 1
total operation: 1
analogous description: 1
finitely multipresentable category: 1
countable coproduct specification: 1
finite colimit specification: 1
abelian tensor product: 1
compatible action: 1
symmetric biclosed monoidal category: 1
biclosed monoidal category: 1
cofree object: 1
normal subgroup: 1
second homotopy module: 1
certain homotopy pushout: 1
several new situation: 1
new situation: 1
noncommutative logic: 1
noncommutative version: 1
essential difference: 1
certain tensorial strength: 1
tensorial strength: 1
appropriate categorical structure: 1
corresponding categorical structure: 1
general coherence theorem: 1
lax operad action: 1
strict action: 1
familiar coherence result: 1
many new one: 1
lax module: 1
such ring: 1
pure relational language: 1
relational language: 1
same first order sentence: 1
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