Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids

Simona Paoli

doi:10.1016/j.jpaa.2007.04.006

Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids

Simona Paoli^*

^*Corresponding author for this work

Mathematical Science

Macquarie University

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

3 Citations (Scopus)

Abstract

Homotopy 3-types can be modelled algebraically by Tamsamani's weak 3-groupoids as well as, in the path-connected case, by cat²-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two different semistrict algebraic models of connected 3-types using Tamsamani's model. Both are then related to Gray groupoids.

Original language	English
Pages (from-to)	801-820
Number of pages	20
Journal	Journal of Pure and Applied Algebra
Volume	211
Issue number	3
Early online date	29 Apr 2007
DOIs	https://doi.org/10.1016/j.jpaa.2007.04.006
Publication status	Published - Dec 2007

Bibliographical note

Funding Information:
I am grateful to Michael Batanin and Clemens Berger for helpful conversations. I also thank the members of the Australian Category Seminar for support and encouragement, and the referee for some remarks on literature sources. This work was supported by an Australian Research Council Postdoctoral Fellowship (project no. DP0558598).

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10.1016/j.jpaa.2007.04.006

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abstract = "Homotopy 3-types can be modelled algebraically by Tamsamani's weak 3-groupoids as well as, in the path-connected case, by cat2-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two different semistrict algebraic models of connected 3-types using Tamsamani's model. Both are then related to Gray groupoids.",

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note = "Funding Information: I am grateful to Michael Batanin and Clemens Berger for helpful conversations. I also thank the members of the Australian Category Seminar for support and encouragement, and the referee for some remarks on literature sources. This work was supported by an Australian Research Council Postdoctoral Fellowship (project no. DP0558598). ",

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AB - Homotopy 3-types can be modelled algebraically by Tamsamani's weak 3-groupoids as well as, in the path-connected case, by cat2-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two different semistrict algebraic models of connected 3-types using Tamsamani's model. Both are then related to Gray groupoids.

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ER -

Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids

Abstract

Bibliographical note

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