Exact categories |
| |
Authors: | Theo Bühler |
| |
Institution: | FIM, HG G39.5, Rämistrasse 101, 8092 ETH Zürich, Switzerland |
| |
Abstract: | We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any embedding into abelian categories and we sketch Deligne's approach to derived functors. The construction of classical derived functors with values in an abelian category painlessly translates to exact categories, i.e., we give proofs of the comparison theorem for projective resolutions and the horseshoe lemma. After discussing some examples we elaborate on Thomason's proof of the Gabriel–Quillen embedding theorem in an appendix. |
| |
Keywords: | primary 18-02 secondary 18E10 18E30 |
本文献已被 ScienceDirect 等数据库收录! |
|