Canonical resolutions in hereditary abelian model categories

James Gillespie

Vol. 313 (2021), No. 2, 365–411

DOI: 10.2140/pjm.2021.313.365

Abstract

Each object of any abelian model category has a canonical resolution, as described in this article. When the model structure is hereditary we show how morphism sets in the associated homotopy category may be realized as cohomology groups computed from these resolutions. We also give an alternative description of the morphism sets in terms of Yoneda Ext groups.

Keywords

abelian model category, canonical resolution

Mathematical Subject Classification 2010

Primary: 18E10, 18G25, 18G55

Secondary: 55U35

Milestones

Received: 13 February 2020

Accepted: 16 March 2021

Published: 12 October 2021