We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an Abelian monoidal category M. If M is also cocomplete, complete, and AB5, we show that such a cotensor coalgebra exists and satisfies a meaningful universal property which resembles the classical one. Here the lack of the coradical filtration is filled by considering a direct limit of a filtration consisting of wedge products. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.

Cotensor Coalgebras in Monoidal Categories

ARDIZZONI, Alessandro;
2007-01-01

Abstract

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an Abelian monoidal category M. If M is also cocomplete, complete, and AB5, we show that such a cotensor coalgebra exists and satisfies a meaningful universal property which resembles the classical one. Here the lack of the coradical filtration is filled by considering a direct limit of a filtration consisting of wedge products. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.
2007
35
25
70
http://arxiv.org/pdf/math/0507334.pdf
http://dx.doi.org/10.1080/00927870600936856
Colimits; Cotensor coalgebras; Monoidal categories; Wedge products
A. ARDIZZONI; C. MENINI; D. STEFAN
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/93214
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