Lifting theorems for Kleisli categories Export

@incollection{Mulry94KleisliLifting, 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.}, author = {Mulry, Philip}, citeulike-article-id = {4916974}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/3-540-58027-1_15}, citeulike-linkout-1 = {http://www.springerlink.com/content/f3276117u877t763}, doi = {10.1007/3-540-58027-1_15}, journal = {Mathematical Foundations of Programming Semantics}, keywords = {category\_theory, functor\_lifting, kleisli\_category}, pages = {304--319}, posted-at = {2009-06-20 10:31:30}, priority = {2}, title = {Lifting theorems for Kleisli categories}, url = {http://dx.doi.org/10.1007/3-540-58027-1_15}, year = {1994} }

TY - CHAP ID - Mulry94KleisliLifting L3 - citeulike-article-id:4916974 N2 - 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. JF - Mathematical Foundations of Programming Semantics EP - 319 TI - Lifting theorems for Kleisli categories SP - 304 KW - category_theory KW - functor_lifting KW - kleisli_category AU - Mulry, Philip PY - 1994/// UR - http://dx.doi.org/10.1007/3-540-58027-1_15 ER -