Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929476628119552 |
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| author | Ruit, Jaco |
| author_facet | Ruit, Jaco |
| contents | We study the framework of $\infty$-equipments which is designed to produce well-behaved theories for different generalizations of $\infty$-categories in a synthetic and uniform fashion. We consider notions of (lax) functors between these equipments, closed monoidal structures on these equipments, and fibrations internal to these equipments. As a main application, we will demonstrate that the foundations of internal $\infty$-category theory can be readily obtained using this formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations Ruit, Jaco Category Theory Algebraic Topology 18D65, 18D70, 18N65, 55U35, 18N10 We study the framework of $\infty$-equipments which is designed to produce well-behaved theories for different generalizations of $\infty$-categories in a synthetic and uniform fashion. We consider notions of (lax) functors between these equipments, closed monoidal structures on these equipments, and fibrations internal to these equipments. As a main application, we will demonstrate that the foundations of internal $\infty$-category theory can be readily obtained using this formalism. |
| title | Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations |
| topic | Category Theory Algebraic Topology 18D65, 18D70, 18N65, 55U35, 18N10 |
| url | https://arxiv.org/abs/2408.15190 |