# Cotensor Coalgebras in Monoidal Categories

Research paper by A. Ardizzoni, C. Menini, D. Stefan

Indexed on: 16 Jul '05Published on: 16 Jul '05Published in: Mathematics - Quantum Algebra

#### Abstract

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth.