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.