Notions of enriched purity
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Theory and Applications of Categories |
| MU Faculty or unit | |
| Citation | |
| web | http://www.tac.mta.ca/tac/volumes/41/58/41-58abs.html |
| Keywords | enriched accessible categories; enriched purity; enriched injectivity classes |
| Description | 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, ?-complete posets, and quasivarieties, we characterize the (?, E)-injectivity classes of locally presentable V-categories in terms of closure under a class of limits, ?-filtered colimits, and (?,E)-pure subobjects. |
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