Equipping weak equivalences with algebraic structure

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114465" target="_blank" >RIV/00216224:14310/20:00114465 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00209-019-02305-w" target="_blank" >https://doi.org/10.1007/s00209-019-02305-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-019-02305-w" target="_blank" >10.1007/s00209-019-02305-w</a>

Result language
angličtina
Original language name
Equipping weak equivalences with algebraic structure
Original language description
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure if and only it is a weak homotopy equivalence. Likewise for quasi-isomorphisms and many other examples. The basic trick is to consider injectivity in arrow categories. Using algebraic injectivity and cone injectivity we obtain general results about the extent to which the weak equivalences in a combinatorial model category can be equipped with algebraic structure.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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