Exact Categories

  title={Exact Categories},
  author={Theo B Uhler},
  • Theo B Uhler
  • Published 2008
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. The construction of classical derived functors with values in an… CONTINUE READING