Vol. 313, No. 2, 2021

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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
Authors
James Gillespie
School of Theoretical and Applied Science
Ramapo College of New Jersey
Mahwah, NJ 07430
United States