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2001 Semidirect products of categorical groups. Obstruction theory
Antonio R. Garzón, Hvedri Inassaridze
Homology Homotopy Appl. 3(1): 111-138 (2001).

Abstract

By considering the notion of action of a categorical group ${\mathbb G}$ on another categorical group ${\mathbb H}$ we define the semidirect product ${\mathbb H}\ltimes {\mathbb G}$ and classify the set of all split extensions of ${\mathbb G}$ by ${\mathbb H}$. Then, in an analogous way to the group case, we develop an obstruction theory that allows the classification of all split extensions of categorical groups inducing a given pair $(\varphi,\psi)$ (called a collective character of ${\mathbb G}$ in ${\mathbb H}$) where $\varphi:\pi_0({\mathbb G})\rightarrow \pi_0({\cal E}q({\mathbb H}))$ is a group homomorphism and $\psi:\pi_1({\mathbb G})\rightarrow \pi_1({\cal E}q({\mathbb H}))$ is a homomorphism of $\pi_0({\mathbb G})$-modules.

Citation

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Antonio R. Garzón. Hvedri Inassaridze. "Semidirect products of categorical groups. Obstruction theory." Homology Homotopy Appl. 3 (1) 111 - 138, 2001.

Information

Published: 2001
First available in Project Euclid: 19 February 2006

zbMATH: 0984.18005
MathSciNet: MR1854641

Subjects:
Primary: 18D10
Secondary: 18G50

Rights: Copyright © 2001 International Press of Boston

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Vol.3 • No. 1 • 2001
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