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Grothendieck $\infty$-groupoids, and still another definition of $\infty$-categories

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arxiv 1009.2331 v1 pith:G4A5MOZL submitted 2010-09-13 math.CT math.AT

Georges Maltsiniotis This is my paper · ORCID
classification math.CTmath.AT
keywords inftygrothendieckcategoriesdefinitionanotherapproachdevelopedgroupoid
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abstract

The aim of this paper is to present a simplified version of the notion of $\infty$-groupoid developed by Grothendieck in "Pursuing Stacks" and to introduce a definition of $\infty$-categories inspired by Grothendieck's approach.

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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. Semi-strictification of $(\infty, n)$-categories

    math.CT 2025-06 conditional novelty 8.0 of 10

    Every weak (∞,n)-category embeds into a semi-strict algebraic model via an acyclic cofibration, forming the derived unit of a Quillen equivalence between weak model categories.

  2. Computads with invertible generators for weak {\omega}-categories

    math.CT 2026-06 unverdicted novelty 7.0 of 10

    Extends computads with invertible generators, constructs a coreflection to ordinary computads that preserves generated ω-categories, proves those ω-categories are cofibrant, and shows the subcategory of generalised co...

  3. Naturality for higher-dimensional path types

    math.CT 2025-01 conditional novelty 7.0 of 10

    A depth-bounded naturality meta-operation in the Catt type theory constructs and machine-checks cylinder and cone composites in weak omega-categories.

  4. Algebraic coherators, controlled theories, and Grothendieck realizations

    math.CT 2026-07 conditional novelty 5.5 of 10

    Algebraic coherators and Grothendieck realizations produce infinity-Lawvere theories for monoidal and Picard infinity-groupoids; a generalized pushout conjecture would yield semi-model structures and the Homotopy Hypothesis.

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