  We generalize the notion of ends and coends in category theory to the realm
of module categories over finite tensor categories. We call this new concept
"module (co)end". This tool allows us to give different proofs to several known
results in the theory of representations of finite tensor categories. As a new
application, we present a description of the relative Serre functor for module
categories in terms of a module coend, in a analogous way as a Morita invariant
description of the Nakayama functor of abelian categories presented in [J.
Fuchs, G. Schaumann and C. Schweigert, Eilenberg-Watts calculus for finite
categories and a bimodule Radford S^4 theorem, Trans. Amer. Math. Soc. 373
(2020), 1-40]

Quantum Algebra;Category Theory