Homology, Homotopy and Applications
Volume 24 (2022)
Algebraically cofibrant and fibrant objects revisited
Pages: 271 – 298
We extend all known results about transferred model structures on algebraically cofibrant and fibrant objects by working with weak model categories. We show that for an accessible weak model category there are always Quillen equivalent transferred weak model structures on both the categories of algebraically cofibrant and algebraically fibrant objects. Under additional assumptions, these transferred weak model structures are shown to be left, right or Quillen model structures. By combining both constructions, we show that each combinatorial weak model category is connected, via a chain of Quillen equivalences, to a combinatorial Quillen model category in which all objects are fibrant.
2010 Mathematics Subject Classification
18C35, 18G55, 55U35
The first-named author acknowledges the support of the Grant Agency of the Czech Republic under the grant 19-00902S.
Received 14 May 2020
Received revised 23 May 2021
Accepted 1 June 2021
Published 13 April 2022