Algebraic weak factorisation systems II: categories of weak maps

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Algebraic weak factorisation systems II: categories of weak maps

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Algebraic weak factorisation systems II: categories of weak maps

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

—

Svazek periodika

220

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

27

Strana od-do

148-174

Kód UT WoS článku

000362138300007

EID výsledku v databázi Scopus

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