homological algebra
and
nonabelian homological algebra
additive and abelian categories
Ab-enriched category
pre-additive category
additive category
pre-abelian category
abelian category
Grothendieck category
abelian sheaves
semi-abelian category
kernel, cokernel
complex
differential
homology
category of chain complexes
chain complex
chain map, quasi-isomorphism
chain homotopy
chain homology and cohomology
exact sequence,
injective object, projective object
injective resolution, projective resolution
flat resolution
derived functor
Tor, Ext
homotopy limit, homotopy colimit
abelian sheaf cohomology
derived category
triangulated category, enhanced triangulated category
stable (∞,1)-category
stable model category
pretriangulated dg-category
A-∞-category
(∞,1)-category of chain complexes
double complex
Koszul-Tate resolution, BRST-BV complex
spectral sequence
spectral sequence of a filtered complex
spectral sequence of a double complex
Grothendieck spectral sequence
Leray spectral sequence
Serre spectral sequence
Hochschild-Serre spectral sequence
diagram chasing
3x3 lemma
four lemma, five lemma
snake lemma, connecting homomorphism
horseshoe lemma
Baer's criterion
singular homology
cyclic homology
Dold-Kan correspondence / monoidal, operadic
Eilenberg-Zilber theorem
universal coefficient theorem
Künneth theorem
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(∞,1)-category theory
category theory
higher category theory
(n,r)-category
(∞,1)-category
hom-objects
equivalences in/of (∞,1)-categories
sub-(∞,1)-category
reflective sub-(∞,1)-category
reflective localization
opposite (∞,1)-category
over (∞,1)-category
(∞,1)-functor
exact (∞,1)-functor
(∞,1)-category of (∞,1)-functors
(∞,1)-category of (∞,1)-presheaves
fibrations
inner fibration
left/right fibration
Cartesian fibration
limit
adjoint functors
locally presentable
essentially small
locally small
accessible
idempotent-complete
(∞,1)-Yoneda lemma
(∞,1)-Grothendieck construction
adjoint (∞,1)-functor theorem
(∞,1)-monadicity theorem
(∞,1)-topos
category with weak equivalences
model category
derivator
quasi-category
model structure for quasi-categories
model structure for Cartesian fibrations
relation to simplicial categories
homotopy coherent nerve
simplicial model category
presentable quasi-category
Kan complex
An (∞,1)-category presented by a model structure on chain complexes.
Its homotopy category of an (∞,1)-category is the derived category of the underlying abelian category.
stable (∞,1)-category, triangulated category
truncation of a chain complex, suspension of a chain complex