In mathematics, the category Grp has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory.
In mathematics, specifically in the field known as category theory, a monoidal category where the monoidal product is the categorical product is called a cartesian monoidal category. Any category with...
In category theory, a branch of mathematics, a pullback is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is...
In 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...
In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: indeed, every small abelian category can...
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism R : A → B in this category is a relation between...
In category theory, a branch of mathematics, a closed category is a special kind of category. In a locally small category, the external hom maps a pair of objects to...
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 monoidal category. It is motivated by...
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 category C. Given a statement...
In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion...
