the notion of self-adjunction, which we have investigated in [@DP03]. A self-adjunction is an adjoint situation where an endofunctor is both left and right adjoint to itself. So we find a close relationship between Frobenius monads and self-adjunctions. Through this relationship, we can prove coherence results for Frobenius monads, by relying on a coherence result that we have previously established for self-adjunctions. (That self-adjunction arises in the context of Frobenius monads was noted in [@RSW05], Note after Definition 2.9; this is however implicit already in [@LAW69], pp. 151-152, in [@CW87], Theorem 2.4, and in [@K03], Chapter 2.)

These coherence results assert that there is a faithful functor from a freely generated Frobenius monad to manageable model categories, which we will consider in this paper. This faithful functor is here an isomorphism. With our model categories we can easily decide whether a diagram of arrows commutes. In logical terms, this is like proving completeness with respect to a manageable model, which helps us to solve the decision problem. Coherence here is analogous to the isomorphism that exists between the syntactically constructed freely generated monad and the simplicial category (see [@DP08b], Section 3, [@D08], Section 4, and references therein).

The coherence we 