category theory
category
functor
natural transformation
Cat
universal construction
representable functor
adjoint functor
limit/colimit
weighted limit
end/coend
Kan extension
Yoneda lemma
Isbell duality
Grothendieck construction
adjoint functor theorem
monadicity theorem
adjoint lifting theorem
Tannaka duality
Gabriel-Ulmer duality
small object argument
Freyd-Mitchell embedding theorem
sheaf and topos theory
enriched category theory
higher category theory
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homotopy theory
k-morphism, coherence
looping and delooping
looping and suspension
homotopy hypothesis-theorem
delooping hypothesis-theorem
periodic table
stabilization hypothesis-theorem
exactness hypothesis
holographic principle
applications of (higher) category theory
higher category theory and physics
(n,r)-category
Theta-space
∞-category/ω-category
(∞,n)-category
(∞,2)-category
(∞,1)-category
quasi-category
simplicially enriched category
complete Segal space
model category
(∞,0)-category/∞-groupoid
Kan complex
algebraic Kan complex
simplicial T-complex
n-category = (n,n)-category
2-category, (2,1)-category
1-category
0-category
(−1)-category
(−2)-category
n-poset = (n-1,n)-category
poset = (0,1)-category
2-poset = (1,2)-category
n-groupoid = (n,0)-category
categorification/decategorification
geometric definition of higher category
simplicial model for weak ω-categories
complicial set
weak complicial set
algebraic definition of higher category
bicategory
bigroupoid
tricategory
tetracategory
strict ω-category
Batanin ω-category
Trimble ω-category
Grothendieck-Maltsiniotis ∞-categories
stable homotopy theory
symmetric monoidal category
symmetric monoidal (∞,1)-category
stable (∞,1)-category
dg-category
A-∞ category
triangulated category
k-morphism
transfor
modification
2-functor
pseudofunctor
lax functor
(∞,1)-functor
2-limit
(∞,1)-adjunction
(∞,1)-Kan extension
(∞,1)-Grothendieck construction
cosmic cube
k-tuply monoidal n-category
strict ∞-category, strict ∞-groupoid
(∞,1)-topos
homotopical category
model category theory
effective epimorphism ⇒ regular epimorphism ⇔ covering
effective monomorphism ⇒ regular monomorphism ⇔ embedding .
See cover, covering space.