In category theory, a Kleisli category is a category naturally associated to any monad T. It is equivalent to the category of free T-algebras. The Kleisli...

Tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C...

prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...

Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

constructions in category theory, including the Kleisli category and Kleisli triples. He is also the namesake of the Kleisli Query System, a tool for integration...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

Eilenberg–Moore category C T {\displaystyle C^{T}} is a terminal object in A d j ( C , T ) {\displaystyle \mathbf {Adj} (C,T)} . An initial object is the Kleisli category...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

above fashion. Two constructions, called the category of Eilenberg–Moore algebras and the Kleisli category are two extremal solutions to the problem of...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept...

this means any monad both gives rise to a category (called the Kleisli category) and a monoid in the category of functors (from values to computations)...

proved that any equaliser in any category is a monomorphism. If the converse holds in a given category, then that category is said to be regular (in the...

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general...

In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms:...