Doctrines Whose Structure Forms a Fully Faithful Adjoint String

  title={Doctrines Whose Structure Forms a Fully Faithful Adjoint String},
  author={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. 
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