ANDRÉ-QUILLEN COHOMOLOGY AND k-INVARIANTS OF SIMPLICIAL CATEGORIES

David Blanc; Nicholas J. Meadows

doi:10.4310/HHA.2025.V27.N1.A9

ANDRÉ-QUILLEN COHOMOLOGY AND k-INVARIANTS OF SIMPLICIAL CATEGORIES

David Blanc, Nicholas J. Meadows

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 André-Quillen cohomology groups in which the k-invariants for X take value. Given a map of simplicial categories ϕ: 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 ϕ to P⁽ⁿ⁾X.

Original language	English
Pages (from-to)	147-177
Number of pages	31
Journal	Homology, Homotopy and Applications
Volume	27
Issue number	1
DOIs	https://doi.org/10.4310/HHA.2025.V27.N1.A9
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025, International Press.

Keywords

cohomology
k-invariant
simplicial category
∞-category

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4310/HHA.2025.V27.N1.A9

Cite this

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N2 - Exploiting the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category X, we obtain a cochain complex for the André-Quillen cohomology groups in which the k-invariants for X take value. Given a map of simplicial categories ϕ: 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 ϕ to P(n)X.

AB - Exploiting the Harpaz-Nuiten-Prasma interpretation of the Dwyer-Kan-Smith cohomology of a simplicial category X, we obtain a cochain complex for the André-Quillen cohomology groups in which the k-invariants for X take value. Given a map of simplicial categories ϕ: 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 ϕ to P(n)X.

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KW - simplicial category

KW - ∞-category

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JO - Homology, Homotopy and Applications

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IS - 1

ER -

ANDRÉ-QUILLEN COHOMOLOGY AND k-INVARIANTS OF SIMPLICIAL CATEGORIES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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