Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Behavior of Quillen (co)homology with respect to adjunctions

Pages: 67 – 109

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n1.a3


Martin Frankland (Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario, Canada)


This paper aims to answer the following question: Given an adjunction between two categories, how is Quillen (co)homology in one category related to that in the other? We identify the induced comparison diagram, giving necessary and sufficient conditions for it to arise, and describe the various comparison maps. Examples are given. Along the way, we clarify some categorical assumptions underlying Quillen (co)homology: cocomplete categories with a set of small projective generators provide a convenient setup.


Quillen, homology, cohomology, adjunction, simplicial, model structure, comparison

2010 Mathematics Subject Classification

13D03, 18G30, 18G55, 55U35

Published 18 May 2015