Pith. sign in

REVIEW 3 cited by

Presentable (infty, n)-categories

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2011.03035 v1 pith:BQJBEJCP submitted 2020-11-05 math.AT math.CT

Presentable (infty, n)-categories

classification math.AT math.CT
keywords inftycategoriesconicalmathcalpresentablecategorycolimitsmathrm
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We define for each $n \geq 1$ a symmetric monoidal $(\infty, n+1)$-category $n\mathrm{Pr}^L$ whose objects we call presentable $(\infty,n)$-categories, generalizing the usual theory of presentable $(\infty,1)$-categories. We show that each object $\mathcal{C}$ in $n\mathrm{Pr}^L$ has an underlying $(\infty,n)$-category $\psi_n(\mathcal{C})$ which admits all conical colimits, and that conical colimits of right adjointable diagrams in $\psi_n(\mathcal{C})$ can be computed in terms of conical limits after passage to right adjoints.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

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

  1. Higher Semiadditive Character Theory

    math.AT 2026-07 accept novelty 7.0

    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.

  2. Enriched $\infty$-operads as marked algebras

    math.AT 2026-07 accept novelty 7.0

    A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.

  3. An Oriented Street--Roberts Conjecture

    math.AT 2026-06 unverdicted novelty 7.0

    Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.