Doctrines whose structure forms a fully faithful adjoint string

F. Marmolejo

We pursue the definition of a KZ-doctrine in terms of a fully faithful adjoint string Dd -| m -| dD. We give the definition in any Gray-category. The concept of algebra is given as an adjunction with invertible counit. We show that these doctrines are instances of more general pseudomonads. The algebras for a pseudomonad are defined in more familiar terms and shown to be the same as the ones defined as adjunctions when we start with a KZ-doctrine.

Keywords: KZ-doctrines, Pseudomonads, Algebras, Gray-categories.

1991 MSC: 18A35, 18C15, 18C20, 18D05, 18D15, 18D20.

Theory and Applications of Categories, Vol. 3, 1997, No. 2, pp 23-24.

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