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

relation between type theory and category theory

sheaf and topos theory

enriched category theory

higher category theory

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topos theory

(0,1)-topos, Heyting algebra, locale

pretopos

topos

Grothendieck topos

category of presheaves

presheaf

representable presheaf

category of sheaves

site

sieve

coverage, pretopology, topology

sheaf

sheafification

quasitopos

base topos, indexed topos

categorical semantics

internal logic

subobject classifier

natural numbers object

logical morphism

geometric morphism

direct image/inverse image

global sections

geometric embedding

surjective geometric morphism

essential geometric morphism

locally connected geometric morphism

connected geometric morphism

totally connected geometric morphism

étale geometric morphism

open geometric morphism

proper geometric morphism, compact topos

separated geometric morphism, Hausdorff topos

local geometric morphism

bounded geometric morphism

base change

localic geometric morphism

hyperconnected geometric morphism

atomic geometric morphism

topological locale

localic topos

petit topos/gros topos

locally connected topos, connected topos, totally connected topos, strongly connected topos

local topos

cohesive topos

classifying topos

smooth topos

cohomology

homotopy

abelian sheaf cohomology

model structure on simplicial presheaves

higher topos theory

(0,1)-topos

2-topos

2-site

2-sheaf, stack

(∞,1)-topos

(∞,1)-site

(∞,1)-sheaf, ∞-stack, derived stack

Diaconescu's theorem

Barr's theorem

A cotopos with all M-types

M-type

cotopos

Last revised on June 4, 2022 at 05:34:32. See the history of this page for a list of all contributions to it.