#### 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