Enrichment through variation
Enrichment through variation
复制标题
通过变异丰富
DOI：
10.1016/s0022-4049(97)00070-4
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发表时间：
1997
影响因子：
0.8
通讯作者：
A. Power
中科院分区：
文献类型：
--
作者：
R. Gordon;A. Power
我们证明，对于闭合二类别 W，张量 W 类别和它们之间的所有 W 函子的 2 类别等价于闭合 W 表示及其映射的 2 类别，而后者又同构于 Lax(W, Cat) 的完整子 2 类别。我们进一步表明，如果 ω 是 W 的局部稠密子类别，并且 W 是双闭的，则具有 1 个 ω 单元的张量的 W 类别的 2 类别完全嵌入到 ω 表示的 2 类别中。这使我们能够将 Gabriel-Ulmer 对偶性推广到 W 范畴，并证明，对于 W 范畴，对于局部有限可表示的 A 和承认有限张量和过滤余极限的 B，来自 Afto B 的 W 函子的范畴等效于从 A 到 B 的有限 W 函子的范畴。
We show that, for a closed bicategory W, the 2-category of tensored W-categories and all W-functors between them is equivalent to the 2-category of closed W-representations and maps of such, which in turn is isomorphic to a full sub-2-category of Lax(W, Cat). We further show that, if ω is a locally dense subbicategory of W and W is biclosed, then the 2-category of W-categories having tensors with 1-cells of ω embeds fully into the 2-category of ω-representations. This allows us to generalize Gabriel-Ulmer duality to W-categories and to prove, for W-categories, that for locally finitely presentable A and for B admitting finite tensors and filtered colimits, the category of W-functors from Afto B is equivalent to that of finitary W-functors from A to B.