Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads
نویسندگان
چکیده
منابع مشابه
Monads and Adjunctions for Global Exceptions
In this paper, we look at two categorical accounts of computational effects (strong monad as a model of the monadic metalanguage, adjunction as a model of call-bypush-value with stacks), and we adapt them to incorporate global exceptions. In each case, we extend the calculus with a construct, due to Benton and Kennedy, that fuses exception handling with sequencing. This immediately gives us an ...
متن کاملMonads Defined by Involution - Preserving Adjunctions
Consider categories with involutions which fix objects, functors which preserve involution, and natural transformations. In this setting certain natural adjunctions become universal and, thereby, become constructible from abstract data. Although the formal theory of monads fails to apply and the Eilenberg-Moore category fails to fit, both are successfully adapted to this setting, which is a 2-c...
متن کاملCategories Enriched over a Quantaloid: Isbell Adjunctions and Kan Adjunctions
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory. It is proved that these two processes are functorial with infomorphisms playing as morphi...
متن کاملHomotopy Coherent Adjunctions and the Formal Theory of Monads
In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterise its n-arrows using a graphical calculus that we develop here. The hom-spaces are appropriately fibrant, indeed are nerves of categories, which indicates that all of the expected coherence equations in each dimension are present. To justify our terminology, we prove tha...
متن کاملEquational presentations of functors and monads
In categorical universal algebra, it is well known that a finitary equational presentation of algebras in a finitary variety K amounts to the existence of a coequaliser of a pair of morphisms between finitely generated free algebras. The essence of a universal-algebraic flavour of a finitary functor L : K −→ K is that L is determined by its behaviour on finitely generated free algebras. In fact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1993
ISSN: 0022-4049
DOI: 10.1016/0022-4049(93)90092-8