nLab
free resolution

Idea

The resolution of a chain complex be a complex of free modules.

Properties

Existence

Proposition

For $R$ a ring, every $R$-module admits a free resolution.

Related concepts

• projective object, projective presentation, projective cover, projective resolution

  • projective module

• injective object, injective presentation, injective envelope, injective resolution

  • injective module

• free object, free resolution

  • free module

• flat object, flat resolution

  • flat module

References

Lecture notes include for instance

around page 5 of

• Andrew Baker?, Notes on chain complexes (pdf)