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Notes on weak units of group-like 1- and 2-stacks

Published online by Cambridge University Press:  09 November 2016

ETTORE ALDROVANDI  and
A. EMIN TATAR
ETTORE ALDROVANDI
Affiliation:
Department of Mathematics, Florida State University, 1017 Academic Way Tallahassee, FL 32312-4510, U.S.A. e-mail: [email protected]
A. EMIN TATAR
Affiliation:
Department of Mathematics and Statistics, KFUPM, Dhahran, 31261, Saudi Arabia. e-mail: [email protected]
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Abstract

The weak units of strict monoidal 1- and 2-categories are defined respectively in [15] and [14]. In this paper, we define them for group-like 1- and 2-stacks. We show that they form a contractible Picard 1- and 2-stack, respectively. We give their cohomological description which provides for these stacks a representation by complexes of sheaves of groups. Later, we extend the discussion to the monoidal case. We consider the (2-)substack of cancelable objects of a monoidal 1-(2-)stack. We observe that this (2-)substack is trivially group-like, its weak units are the same as the weak units of the monoidal 1-(2-)stack, and therefore we can recover the contractibility results in [15] and [14] by analysing it.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 2 , March 2018 , pp. 205 - 220
Copyright
Copyright © Cambridge Philosophical Society 2016 

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