Algebraic weak factorisation systems II: categories of weak maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00087740" target="_blank" >RIV/00216224:14310/16:00087740 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2015.06.003" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2015.06.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2015.06.003" target="_blank" >10.1016/j.jpaa.2015.06.003</a>

Result language
angličtina
Original language name
Algebraic weak factorisation systems II: categories of weak maps
Original language description
We investigate the categories of weak maps associated to an algebraic weak factorisation system (awfs) in the sense of Grandis–Tholen [14]. For any awfs on a category with an initial object, cofibrant replacement forms a comonad, and the category of (left) weak maps associated to the awfs is by definition the Kleisli category of this comonad. We exhibit categories of weak maps as a kind of “homotopy category”, that freely adjoins a section for every “acyclic fibration” (= right map) of the awfs; and using this characterisation, we give an alternate description of categories of weak maps in terms of spans with left leg an acyclic fibration. We moreover show that the 2-functor sending each awfs on a suitable category to its cofibrant replacement comonad has a fully faithful right adjoint: so exhibiting the theory of comonads, and dually of monads, as incorporated into the theory of awfs.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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