论文标题
工作主角的活动
Actegories for the Working Amthematician
论文作者
论文摘要
很长一段时间以来，类别对类别（也称为Actegories）的类别的行动已经对类别理论家熟悉，但文献中似乎缺少对该主题的全面概述。最近，Actegories越来越多地在应用类别理论中使用，从而鼓励根据这些应用程序的新需求来填补这一空白。这项工作始于对单型敏感性的概念的研究，这是一对兼容的单型和驱动结构，最终包括对actegories基本理论的相当大的参考。我们涵盖了当然的基本定义和结果，这些定义和结果明确阐明了许多民俗定义，包括其张量产品和他们的hom-tensor相连。我们给出了具有单体，编织的单体和对称单体结构的新定义。在最后一节中，我们为这些结构提供了三个类似开贝的分类结果。
Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic seems to be missing from the literature. Recently, actegories have been increasingly employed in applied category theory, thereby encouraging an effort to fill this gap according to the new needs of these applications. This work started as an investigation of the notion of monoidal actegory, a compatible pair of monoidal and actegorical structures, and ended up including a sizable reference on the elementary theory of actegories. We cover basic definitions and results on actegories and biactegories, spelling out explicitly many folkloric definitions, including their tensor product and their hom-tensor adjunction. We give new definitions of actegories with monoidal, braided monoidal and symmetric monoidal structure. In the last section, we provide three Cayley-like classification results for these structures.
