Enriched bi(co)ends

Abstract

In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched (co)ends, which can be found in [Kel05] or in the more recent [Lor21]. One of the main obstacles to the construction of such a theory is the amount of structure involved at this stage of categorification. A great help will be furnished by strictification results (Section 2), as well as the powerful tool of string diagrams (Section 3), essential for making calculations manageable by a human being.