Formal category theory in $\infty$-equipments I
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911174592823296 |
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| author | Ruit, Jaco |
| author_facet | Ruit, Jaco |
| contents | We generalize proarrow equipments from strict category theory to the $\infty$-categorical setting, introducing the concept of $\infty$-equipments. These are specific double $\infty$-categories that support an internal higher category theory. This paper explores several examples of $\infty$-equipments, including the prototypical example of the $\infty$-equipment of $\infty$-categories and the more general $\infty$-equipments of internal $\infty$-categories. The ultimate objective of this article is to study the basic concepts of category theory within an arbitrary $\infty$-equipment, such as colimits and Kan extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Formal category theory in $\infty$-equipments I Ruit, Jaco Category Theory Algebraic Topology 18D65, 18D70, 18N10, 55U35, 18N65 We generalize proarrow equipments from strict category theory to the $\infty$-categorical setting, introducing the concept of $\infty$-equipments. These are specific double $\infty$-categories that support an internal higher category theory. This paper explores several examples of $\infty$-equipments, including the prototypical example of the $\infty$-equipment of $\infty$-categories and the more general $\infty$-equipments of internal $\infty$-categories. The ultimate objective of this article is to study the basic concepts of category theory within an arbitrary $\infty$-equipment, such as colimits and Kan extensions. |
| title | Formal category theory in $\infty$-equipments I |
| topic | Category Theory Algebraic Topology 18D65, 18D70, 18N10, 55U35, 18N65 |
| url | https://arxiv.org/abs/2308.03583 |