Australian Category Seminar

Definable Enriched Categories

Giacomo Tendasยท1 May 2019

Picking up where we left off at my previous talk, we introduce an enriched notion of definable category. Then, if our base for enrichment is a symmetric monoidal finitary variety, we can prove a duality between the 2-category V-Ex of small exact V-categories, and V-Def of definable V-categories, generalizing the ordinary result of Kuber-Rosicky, and the additive version of Prest-Rajani. We then use this to give an explicit description of the free exact completions over finitely complete V-categories and over regular V-categories.

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