Flatness, weakly lex colimits, and free exact completions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139325" target="_blank" >RIV/00216224:14310/24:00139325 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10231-023-01383-2" target="_blank" >https://doi.org/10.1007/s10231-023-01383-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-023-01383-2" target="_blank" >10.1007/s10231-023-01383-2</a>

Result language
angličtina
Original language name
Flatness, weakly lex colimits, and free exact completions
Original language description
We capture in the context of lex colimits, introduced by Garner and Lack, the universal property of the free regular and Barr-exact completions of a weakly lex category. This is done by introducing a notion of flatness for functors $$F:{{mathcal {C}}}rightarrow {{mathcal {E}}}$$with lex codomain, and using this to describe the universal property of free $$Phi $$-exact completions in the absence of finite limits, for any given class $$Phi $$of lex weights. In particular, we shall give necessary and sufficient conditions for the existence of free lextensive and free pretopos completions in the non-lex world, and prove that the ultraproducts, in the categories of models of such completions, satisfy an universal property.
Czech name
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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/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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