Dear categorists, Could you help me by pointing out a reference for the following situation: consider two categories C and D and monads H:C-->C and K:D-->D. Let T:C-->D be a functor having left and right adjoint non-isomorphic. Assume that exists a lifting of T to the Eilenberg-Moore categories of algebras T^:Alg(M)-->Alg(N), corresponding to a distributive law lambda: KT=>TH. Suppose Alg(H) has reflexive coequalizers and lambda is an isomorphism. Then according to Johnstone, Adjoint lifting theorems for categories of algebras, T^ has both left and right adjoints. My question is the following: under which conditions the left and right adjoints of T^ are isomorphic (i. e. T^ is a Frobenius functor)? Has anyone already considered this situation? This is my first time using this mailing list, and I would appreciate any help. Thanks, Adriana Balan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]