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Nerves of enriched categories via necklaces

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arxiv 2408.10049 v2 pith:MLGXXT6A submitted 2024-08-19 math.CT

Arne Mertens This is my paper · ORCID
classification math.CT
keywords nervenecklicialcategoriescubicalenrichednervesapplicationarxiv
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We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical nerves. It is shown that every necklicial nerve can be lifted to the templicial objects of arXiv:2302.02484v2. Building on the work of Dugger and Spivak, we give sufficient conditions under which the left-adjoint of a necklicial nerve can be described more explicitly. As an application, we obtain novel and simple expressions for the left-adjoints of the dg-nerve and cubical nerve.

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Cited by 1 Pith paper

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  1. Lectures on bar and cobar

    math.AT 2025-07 conditional novelty 7.0 of 10

    The author unifies classical and derived bar and cobar constructions via twisted arrow categories of infinity-operads, giving new existence proofs and recovering classical comparison maps.

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