André-Quillen cohomology and $k$-invariants of simplicial categories

Exploiting the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category X , we obtain a cochain complex for the Andr-Quillen cohomology groups in which the k-invariants for X take value.Given a map of simplicial categories : Y P (n-1) X into a Postnikov section of X , we use a homotopy colimit decomposition of Y to study the obstruction to lifting to P (n) X .

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Publication Details

Journal
Homology Homotopy and Applications
Published
2025-01-01
DOI
https://doi.org/10.4310/hha.2025.v27.n1.a9
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
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article

André-Quillen cohomology and $k$-invariants of simplicial categories

Nicholas J. Meadows, David Le Blanc
Homology Homotopy and Applications
Homotopy and Cohomology in Algebraic Topology
article

André-Quillen cohomology and $k$-invariants of simplicial categories

Nicholas J. Meadows, David Le Blanc
article en

Abstract

Exploiting the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category X , we obtain a cochain complex for the Andr-Quillen cohomology groups in which the k-invariants for X take value.Given a map of simplicial categories : Y P (n-1) X into a Postnikov section of X , we use a homotopy colimit decomposition of Y to study the obstruction to lifting to P (n) X .

Homology Homotopy and ApplicationsVol. 27(1)
University of Haifa (IL), University of Bologna (IT)
Decent work and economic growth
Openalex Percentile: Top 91%
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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