Categories of representations of coalgebroids
type: Item
instance of: scholarly article
title: Categories of representations of coalgebroids
zbMATH Open document ID: 0968.18004
author: Paddy McCrudden
published in: Advances in Mathematics
publication date: 2001-09-11T00:00:00Z
review text: The paper generalizes the Tannaka-Krein duality for coalgebroids. A coalgebroid over a monoidal category \(\mathcal V\) is an object of the 2-category \({\mathcal V}^{\text{op}}\)-Cat of categories enriched in \({\mathcal V}^{\text{op}}\). A coalgebroid can also be described as a family of objects from a monoidal category \(\mathcal V\), double-indexed by a set \(I\), subject to certain coalgebra-like axioms. The 2-category of Comod\((C)\) of \(C\)-comodules is defined to be the 2-category of profunctors from \(I\) -- the unit \({\mathcal V}^{\text{op}}\)-category -- to \(C\). Its objects can be described as a family of objects from \(\mathcal V\), indexed by the set \(I\), subject to certain comodule-like axioms. It is shown that a coalgebroid \(C\) can be reconstructed from \(\text{Comod}(C)\) and the forgetful bi-functor to the 2-category \(\mathcal V\text{-Act}//\mathcal V\), (which plays the analogous role of the category of vector spaces in the classical Tannaka-Krein duality). Further, a characterization for an object of \(\mathcal V\text{-Act}//\mathcal V\) to be equivalent to \(\text{Comod}(C)\) for a certain coalgebroid \(C\), is given. Illustrating examples are given, which where mainly taken from a work of \textit{B. Pareigis} [J. Algebra 70, 356-374 (1981; Zbl 0463.18003)].
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 16W35
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 1539369
zbMATH Keywords: Tannaka-Krein duality
zbMATH Keywords: coalgebra
zbMATH Keywords: quantum group
MaRDI profile type: Publication
full work available at URL: aima.2000.1926
OpenAlex ID: W1999357689
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DOI: 10.1006/AIMA.2000.1926
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description: scientific article; zbMATH DE number 1539369