this entry is about the textbook

• Charles Weibel, An Introduction to Homological Algebra

on homological algebra.

Contents

1 Chain complexes

• chain complex

2 Derived functors

• derived functor

3 Tor and Ext

Tor and Ext

4 Homological dimension

5 Spectral sequences

• spectral sequence

6 Group homology and cohomology

• group cohomology

7 Lie algebra homology and cohomology

• Lie algebra homology, Lie algebra cohomology

8 Simplicial methods in homological algebra

8.1 Simplicial object

• simplicial object

8.2 Operations on simplicial objects

8.3 Simplicial homotopy groups

• simplicial homotopy group

8.4 The Dold-Kan correspondence

• Dold-Kan correspondence

8.5 The Eilenberg-Zilber theorem

• Eilenberg-Zilber theorem

8.6 Canonical resolutions

• monad(=triple)/bar construction, comonad, classifying space

8.7 Cotriple homology

• bar construction

• monadic descent

8.8 Andre-Quillen Homology and Cohomology

• Kähler differential

• cotangent complex

9 Hochschild and cyclic homology

9.1 Hochschild Homology and Cohomology of Algebras

• Hochschild cohomology

9.2 Derivations, Differentials and Separable Algebra

• derivation

• differential

• separable algebra

9.3 $H^2$, Extensions, Smooth Algebras

• smooth algebra

9.4 Hochschild products

• Hochschild-Kostant-Rosenberg theorem

9.5 Morita Invariance

9.6 Cyclic Homology

• cyclic cohomology

9.7 Group Rings

9.8 Mixed Complexes

9.9 Graded Algebras

9.10 Lie Algebras of Matrices

10 The derived category

• derived category

A Category Theory Language

• category theory

A.1 Categories

• category

A.2 Functors

• functor

A.3 Natural transformations

• natural transformation

A.4 Abelian categories

• abelian category

A.5 Limits and colimits

• limit, colimit

A.6 Adjoint functors

• adjoint functor