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2007•Homology Homotopy and ApplicationsOpen access

Notes on 2-groupoids, 2-groups and crossed modules

Behrang Noohi

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Abstract

This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification.Some of the results proven here are presumably folklore (but do not appear in the literature to the author's knowledge) and some of the results seem to be new.The main technical tool used throughout the paper is the Quillen model structure on the category of 2-groupoids introduced by Moerdijk and Svensson.

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What this paper is about

This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification.Some of the results proven here are presumably folklore (but do not appear in the literature to the author's knowledge) and some of the results seem to be new.The main technical tool used throughout the paper is the Quillen model structure on the category of 2-groupoids introduced by Moerdijk and Svensson.

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OpenAlex reports 56 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification.Some of the results proven here are presumably folklore (but do not appear in the literature to the author's knowledge) and some of the results seem to be new.The main technical tool used throughout the paper is the Quillen model structure on the category of 2-groupoids introduced by Moerdijk and Svensson.

Key concepts: Mathematics, Algebra over a field, Pure mathematics, Sociology

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