Enriched categories as a free cocompletion
Enriched categories as a free cocompletion
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丰富的类别作为免费的补充
DOI：
10.1016/j.aim.2015.11.012
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发表时间：
2013
影响因子：
1.7
通讯作者：
Michael Shulman
中科院分区：
文献类型：
--
作者：
Richard Garner;Michael Shulman
本文有两个目的。第一个是发展在monoidal双范畴中丰富的双范畴理论--将经典的在monoidal范畴中丰富的范畴理论范畴化--直到描述在一类加权双极限下的丰富的双范畴的自由共完成。第二个目标是描述一个万有性质的过程分配给monoidal范畴V的设备V丰富的范畴，函子，变换，和模块;我们这样做是通过考虑，更一般地，分配发送设备C到C-丰富的范畴，函子，变换和模块的设备，并将其表示为在某类加权双极限下的某类丰富双范畴的自由余补。
This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory—categorifying the classical theory of categories enriched in a monoidal category—up to a description of the free cocompletion of an enriched bicategory under a class of weighted bicolimits. The second objective is to describe a universal property of the process assigning to a monoidal category V the equipment of V-enriched categories, functors, transformations, and modules; we do so by considering, more generally, the assignation sending an equipment C to the equipment of C-enriched categories, functors, transformations, and modules, and exhibiting this as the free cocompletion of a certain kind of enriched bicategory under a certain class of weighted bicolimits.