Firm Frobenius monads and firm Frobenius algebras

Böhm, Gabriella Eszter and Gomez-Torrecillas, J. (2013) Firm Frobenius monads and firm Frobenius algebras. SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE. BULLETIN MATHEMATIQUE, 56 (3). pp. 281-298. ISSN 1220-3874

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Abstract

Firm Frobenius algebras are firm algebras and counital coalgebras such that the comultiplication is a bimodule map. They are investigated by categorical methods based on a study of adjunctions and lifted functors. Their categories of comodules and of firm modules are shown to be isomorphic if and only if a canonical comparison functor from the category of comodules to the category of non-unital modules factorizes through the category of firm modules. This happens for example if the underlying algebra possesses local units, e.g. the firm Frobenius algebra arises from a co-Frobenius coalgebra over a base field; or if the comultiplication splits the multiplication (hence the underlying coalgebra is coseparable).

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