In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras a...

We give a direct proof that the category of strict ω-categories is monadic over the category of polygraphs.

The 2-category of constructively completely distributive lattices is shown to be bidual to a 2-category of generalized orders that admits a monadic schizophrenic object biadjunction over the 2-category of ordered sets.

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg–Moore category CT that represents bimorphisms. The category of actions in CT is then shown to be monadic over the base category C.

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg–Moore category CT that represents bimorphisms. The category of actions in CT is then shown to be monadic over the base category C.

We introduce direct categorical models for the computational lambda-calculus. Direct models correspond to the source level of a compiler whose target level corresponds to Moggi’s monadic models. That compiler is a generalised call-by-value CPS-transform. We get our direct models by identifying the algebraic structure on the Kleisli category that arises from a monadic model. We show that direct ...

If S is an order-adjoint monad, that is, a monad on Set that factors through the category of ordered sets with left adjoint maps, then any monad morphism τ : S → T makes T orderadjoint, and the Eilenberg-Moore category of T is monadic over the category of monoids in the Kleisli category of S.

A concept of equation morphism is introduced for every endofuctor F of a cocomplete category C. Equationally defined classes of F–algebras for which free algebras exist are called varieties. Every variety is proved to be monadic over C, and conversely, every monadic category is equivalent to a variety. And the Birkhoff Variety Theorem is proved for “Set–like” categories. By dualizing, we arrive...

In this paper we presented the semantics of database mappings in the relational DB category based on the power-view monad T and monadic algebras. The objects in this category are the database-instances (a database-instance is a set of n-ary relations, i.e., a set of relational tables as in standard RDBs). The morphisms in DB category are used in order to express the semantics of viewbased Globa...

A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent.