homological algebra

(also nonabelian homological algebra)

Introduction

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

chain homotopy

chain homology and cohomology

quasi-isomorphism

homological resolution

simplicial homology

generalized homology

exact sequence,

injective object, projective object

injective resolution, projective resolution

flat resolution

derived category

triangulated category, enhanced triangulated category

stable (∞,1)-category

stable model category

pretriangulated dg-category

A-∞-category

(∞,1)-category of chain complexes

derived functor, derived functor in homological algebra

Tor, Ext

homotopy limit, homotopy colimit

abelian sheaf cohomology

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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Last revised on September 26, 2017 at 15:51:47. See the history of this page for a list of all contributions to it.