index of algebraic topology
- category
- topos
- subspace
- subcategory
- automorphism
- commutative diagram
- concrete category
- dual category
- duality principle
- endomorphism
- epimorphism
- monic
- monomorphism
- source
- pushout
- pullback
- cones and cocones
- limit and colimit functors
- direct sum
- open covers
- isomorphism-closed subcategory
- locally finite category
- preimage of category
- product of categories
- types of morphisms
- wellpowered category
- null object
- zero object
-small
- equalizer
- subobject
- quotient object
- categorical direct product
- categorical direct sum
- direct limit
- limiting cone
- complete category
- groupoid (category theoretic)
- enriched category
- double category
- 2-category
- n-category
- Hurewicz theorem
- cohomology theorems
- homotopy lemma and corollary
- topological space approximation theorem
- Yoneda-Grothendieck Lemma
- van Kampen theorem
- Higher dimensional, generalized van Kampen theorem (HGvKT)
- properties of monomorphisms and epimorphisms
- properties of regular and extremal monomorphisms
- monomorphisms are pullback stable
- proof that an equalizer is a monomorphism
- categorical direct product is an inverse limit
- kernel is an inverse limit
- Grothendieck theorem
- functor
- endofunctor
- category isomorphism
- diagonal functor
- representable functors
- categorical representations
and supergroups
- forgetful functor
- identity functor
- isomorphism
- multifunctor
- natural transformation
- essentially surjective
- faithful functor
- full functor
- adjoint functor
- natural equivalence
- equivalence of categories
- isomorphic categories
- universal properties
- representable functors
- Equivalent definition of a Representable Functor
- simplicial
objects
- preadditive category
- additive category
- abelian category
- non-Abelian categories
and non-Abelian
Algebraic Topology
- supplemental axioms for an Abelian category
- exact sequence
- exact functor
- Grothendieck spectral sequence
- enough projectives
- enough injectives
- projective object
- injective object
- derived functor
- derived category
- Algebraic K-theory
- examples of algebraic K-theory groups
- Grothendieck group
- Grothendieck category
- delta functor
- horseshoe lemma
- syzygy
- Ext
- Tor
- projective dimension
- 5-lemma
- proof of 5-lemma
- 9-lemma
- snake lemma
- proof of snake lemma
- chain homotopy
- chain homotopy equivalence
- chain map
- homology of a chain complex
- Leray spectral sequence
- spectral sequence
- presheaf
- sheaf
- sheafification
- presheaf of a topological basis
- stalk
- Étalé space
- resolution of a sheaf
- gerbes
- site
- small site on a scheme
- topos
- cosmos
- subobject classifier
- well-pointed topos
- power
object
- natural numbers object
- Cartesian closed category
- exponential object
- discrete category
- category example (arrow category)
- category associated to a partial order
- category of matrices
- Category of pseudomorphisms
- Category of intermorphisms
- examples of initial objects and terminal objects and zero objects
- category of sets
- monomorphisms of category of sets
- monoid as a category
- comma category
- category of pointed topological spaces
- simplicial category
- algebra formed from a categories
- monad
- comonad
- monoidal category
- group object
- nerve
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