Enriched categories as a free cocompletion

By Richard Garner, Michael Shulman. 2013

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Abstract This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory—categorifying the classical theory of categories enriched in a monoidal category—up to a description of the free cocompletion of an enriched bicategory under a class of weighted bicolimits. The second objective is to describe a universal property of the process assigning to a monoidal category V the equipment of V -enriched categories, functors, transformations, and modules; we do so by considering, more generally, the assignation sending an equipment C to the equipment of C -enriched categories, functors, transformations, and modules, and exhibiting this as the free cocompletion of a certain kind of enriched bicategory under a certain class of weighted bicolimits.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/389d26eb205de934fe4df655adc2db63e005632f