Ext in pre-Abelian categories

Fred Richman and Elbert A. Walker

Vol. 71 (1977), No. 2, 521–535

DOI: 10.2140/pjm.1977.71.521

Abstract

A natural definition for Ext is given in an arbitrary pre-abelian category. Ext is an additive bifunctor from the category to abelian groups, the five lemma and the 3 × 3 lemma hold, and Extⁿ may be defined in the usual projectiveless way to yield the standard exact sequence of Ext’s. Examples are given of what Ext is in various specific pre-abelian categories.

Mathematical Subject Classification 2000

Primary: 18E05

Milestones

Received: 29 October 1976

Published: 1 August 1977