Abstract
Monads, comonads and categories of algebras have become increasingly important tools in formulating and interpreting concepts in programming language semantics. A natural question that arises is how various categories of algebras for different monads relate functorially. In this paper we investigate when functors between categories with monads or comonads can be lifted to their corresponding Kleisli categories. Determining when adjoint pairs of functors can be lifted or inherited is of particular interest. The results lead naturally to various applications in both extensional and intensional semantics, including work on partial maps and data types and the work of Brookes/Geva on computational comonads.
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