in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...