Geodesic
Doctrines whose structure forms a fully faithful adjoint string
Theory and applications of categories, Tome 3 (1997), pp. 23-24

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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.

Classification : 18A35, 18C15, 18C20, 18D05, 18D15, 18D20.
Keywords: KZ-doctrines, Pseudomonads, Algebras, Gray-categories. 
@article{TAC_1997_3_a1,
     author = {F. Marmolejo},
     title = {Doctrines whose structure forms a fully faithful adjoint string},
     journal = {Theory and applications of categories},
     pages = {23--24},
     publisher = {mathdoc},
     volume = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1997_3_a1/}
}
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F. Marmolejo. Doctrines whose structure forms a fully faithful adjoint string. Theory and applications of categories, Tome 3 (1997), pp. 23-24. http://geodesic.mathdoc.fr/item/TAC_1997_3_a1/