Geodesic
Notions of enriched purity
Theory and applications of categories, Tome 41 (2024), pp. 2058-2104

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We introduce enriched notions of purity depending on the left class E of a factorization system on the base V of enrichment. Ordinary purity is given by the class of surjective mappings in the category of sets. Under specific assumptions, covering enrichment over quantale-valued metric spaces, ω-complete posets, and quasivarieties, we characterize the (λ, E)-injectivity classes of locally presentable V-categories in terms of closure under a class of limits, λ-filtered colimits, and (λ,E)-pure subobjects.

Publié le :
Classification : 18D20, 18C35
Keywords: enriched accessible categories, enriched purity, enriched injectivity classes 
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     author = {Ji\v{r}{\'\i} Rosick\'y and Giacomo Tendas},
     title = {Notions of enriched purity},
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     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a57/}
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Jiří Rosický; Giacomo Tendas. Notions of enriched purity. Theory and applications of categories, Tome 41 (2024), pp. 2058-2104. http://geodesic.mathdoc.fr/item/TAC_2024_41_a57/