Colimits and cocompletions in internal higher category theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914675977879552 |
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| author | Martini, Louis Wolf, Sebastian |
| author_facet | Martini, Louis Wolf, Sebastian |
| contents | We develop a number of basic concepts in the theory of categories internal to an $\infty$-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal property of internal presheaf categories. We furthermore construct the free cocompletion of an internal category by colimits that are indexed by an arbitrary class of diagram shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_14495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Colimits and cocompletions in internal higher category theory Martini, Louis Wolf, Sebastian Category Theory Algebraic Topology We develop a number of basic concepts in the theory of categories internal to an $\infty$-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal property of internal presheaf categories. We furthermore construct the free cocompletion of an internal category by colimits that are indexed by an arbitrary class of diagram shapes. |
| title | Colimits and cocompletions in internal higher category theory |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2111.14495 |