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 computads with generator-preserving morphisms is a presheaf topos.
Grothendieck $\infty$-groupoids, and still another definition of $\infty$-categories
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
math.CT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The inductive coherator models ∞-groupoids, and if model structure transfers succeed successively then the generalized homotopy hypothesis holds.
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Computads with invertible generators for weak {\omega}-categories
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 computads with generator-preserving morphisms is a presheaf topos.
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An Inductive Strategy Towards a Solution to the Generalized Homotopy Hypothesis
The inductive coherator models ∞-groupoids, and if model structure transfers succeed successively then the generalized homotopy hypothesis holds.