论文标题
（CO）张量类别的表示
(Co)ends for representations of tensor categories
论文作者
论文摘要
我们将目的的概念概括为类别理论，而不是有限张量类别的模块类别领域。我们称这个新概念为“模块（CO）结束”。该工具使我们可以在有限张量类别的表示理论中为几个已知结果提供不同的证明。作为一个新应用，我们以模块覆盖的方式介绍了模块类别的相对serre函数的描述，以一种类似的方式作为对[J. Fuchs，G。Schaumann和C. Schweigert，有限类别的Eilenberg-Watts微积分和Bimodule Radford S^4定理，Trans。阿米尔。数学。 Soc。 373（2020），1-40]
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]
