Bimonadicity and the explicit basis property

Matias Menni

Let ${L\dashv R:\cal X \rightarrow\cal Y}$ be an adjunction with $R$ monadic and $L$ comonadic. Denote the induced monad on $\cal Y$ by $M$ and the induced comonad on $\calX$ by $C$. We characterize those $C$ such that $M$ satisfies the Explicit Basis property. We also discuss some new examples and results motivated by this characterization.

Keywords: (co)monads, projective objects, descent, modular categories, Peano algebras

2010 MSC: 18C20, 18E05, 08B20, 08B30

Theory and Applications of Categories, Vol. 26, 2012, No. 22, pp 554-581.

Published 2012-10-18.

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