# nLab Koszul-Tate resolution

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

# Contents

## Idea

For $A$ an algebra and $I \subset A$ an ideal, a Koszul-Tate resolution is a resolution of the quotient $A/I$ by a cochain dg-algebra in non-positive degree that is degreewise free/projective.

It is a refinement of a Koszul complex or rather an extension.

## References

• Jean-Louis Koszul, Homologie et cohomologie des algèbres de Lie , Bulletin de la Société Mathématique de France, 78, 1950, pp 65-127.

• John Tate, Homology of Noetherian rings and local rings , Illinois Journal of Mathematics, 1, 1957, pp. 14-27

Revised on May 11, 2013 17:35:59 by Anonymous Coward (98.114.12.203)