ALGEBRAICALLY COFIBRANT AND FIBRANT OBJECTS REVISITED

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Authors

BOURKE John Denis HENRY Simon

Year of publication 2022
Type Article in Periodical
Magazine / Source Homology, Homotopy and Applications
MU Faculty or unit

Faculty of Science

Citation
Web https://dx.doi.org/10.4310/HHA.2022.v24.n1.a14
Doi http://dx.doi.org/10.4310/HHA.2022.v24.n1.a14
Keywords algebraically cofibrant and fibrant object; weak model category
Description 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.
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