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2003 Bicatégories monoïdales et extensions de gr-catégories
Alain Rousseau
Homology Homotopy Appl. 5(1): 437-547 (2003).

Abstract

In this work, we study the 2-category ${\bf Ext}(\underline{\cal K},\underline{\cal G})$ of extensions of a $gr$-category $\underline{\cal K}$ by a $gr$-category $\underline{\cal G}$. Such an extension consists of a $gr$-category $\underline{\cal H}$, an essentially surjective homomorphism $p : \underline{\cal H} \longrightarrow \underline{\cal K}$ and a monoidal equivalence $q : \underline{\cal G} \longrightarrow N(p)$ where $N(p)$ is the {\it homotopy kernel} of the homomorphism $p$. The main result is a classification theorem which constructs a biequivalence between the 2-category ${\bf Ext}(\underline{\cal K},\underline{\cal G})^{op}$ and the bicategory ${\bf Bimon}(\underline{\cal K}, \underline{\bf Bieq}(\underline{\cal G}))$ of monoidal bicategory homomorphisms between $\underline{\cal K}$ and $\underline{\bf Bieq}(\underline{\cal G})$, where $\underline{\bf Bieq}(\underline{\cal G})$ is the monoidal bicategory of biequivalences of $\underline{\cal G}$ with itself.

Citation

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Alain Rousseau. "Bicatégories monoïdales et extensions de gr-catégories." Homology Homotopy Appl. 5 (1) 437 - 547, 2003.

Information

Published: 2003
First available in Project Euclid: 13 February 2006

zbMATH: 1119.18002
MathSciNet: MR2072344

Subjects:
Primary: 18D05
Secondary: 18D10 , 18G15 , 18G50

Rights: Copyright © 2003 International Press of Boston

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Vol.5 • No. 1 • 2003
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