Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.15190
- arXiv:
- arXiv:2408.15190
- Bibcode:
- 2024arXiv240815190R
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Algebraic Topology;
- 18D65;
- 18D70;
- 18N65;
- 55U35;
- 18N10
- E-Print:
- 67 pages, comments welcome