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2020 Incidence bicomodules, Möbius inversion and a Rota formula for infinity adjunctions
Louis Carlier
Algebr. Geom. Topol. 20(1): 169-213 (2020). DOI: 10.2140/agt.2020.20.169

Abstract

In the same way decomposition spaces, also known as unital 2–Segal spaces, have incidence (co)algebras, and certain relative decomposition spaces have incidence (co)modules, we identify the structures that have incidence bi(co)modules: they are certain augmented double Segal spaces subject to some exactness conditions. We establish a Möbius inversion principle for (co)modules and a Rota formula for certain more involved structures called Möbius bicomodule configurations. The most important instance of the latter notion arises as mapping cylinders of infinity adjunctions, or more generally of adjunctions between Möbius decomposition spaces, in the spirit of Rota’s original formula.

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Louis Carlier. "Incidence bicomodules, Möbius inversion and a Rota formula for infinity adjunctions." Algebr. Geom. Topol. 20 (1) 169 - 213, 2020. https://doi.org/10.2140/agt.2020.20.169

Information

Received: 28 January 2018; Revised: 29 May 2019; Accepted: 24 June 2019; Published: 2020
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/agt.2020.20.169

Subjects:
Primary: 18D05, 18G30, 55U10
Secondary: 06A07, 06A15, 06A75, 16D20, 16T15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 1 • 2020
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