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Categorical Theory of $(\infty,\omega)$-Categories

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arxiv 2406.05425 v2 pith:VR4X6MQW submitted 2024-06-08 math.CT

Félix Loubaton This is my paper · ORCID
classification math.CT
keywords theorycategoriesinftyomegacategoricalcategoryconstructiondedicated
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abstract

This text is dedicated to the development of the theory of $(\infty,\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and lax Kan extensions, among others.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On The Telescopic Picard Group

    math.AT 2024-12 conditional novelty 8.0 of 10

    For all primes p and heights n, Pic(Sp_{T(n)}) contains Z_p × Z/(a_p(p^n−1)), lifting the known K(n)-local subgroup.

  2. Higher Semiadditive Character Theory

    math.AT 2026-07 accept novelty 7.0 of 10

    Every ∞-commutative monoid has a universal (n−t)-fold semiadditive character that blue-shifts height, recovers the transchromatic character on Morava E-theory, and computes L_Q(S^A_{K(n)}) via GL_{n−t}(Z_p)-fixed points.

  3. The Gray Product of $(\infty, n)$-Categories via Lax Grids

    math.CT 2026-06 unverdicted novelty 7.0 of 10

    Univalent Segal sheaves on lax grids are monoidally equivalent to (∞,n)-categories with Campion's Gray product, constructed by Day convolution.

  4. On the squares functor and the Gaitsgory-Rozenblyum conjectures

    math.CT 2025-07 conditional novelty 7.0 of 10

    The authors prove that Gr(Ch×Dv) is naturally equivalent to C⊗D, settling Gaitsgory and Rozenblyum's final conjecture, and establish a companion-based universal property of the squares functor.

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