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ALGEBRAICALLY COFIBRANT AND FIBRANT OBJECTS REVISITED

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BOURKE John Denis HENRY Simon

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj Homology, Homotopy and Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://dx.doi.org/10.4310/HHA.2022.v24.n1.a14
Doi http://dx.doi.org/10.4310/HHA.2022.v24.n1.a14
Klíčová slova algebraically cofibrant and fibrant object; weak model category
Popis 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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