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 be embedded in Ab.
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 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 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...
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 mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is...
In several mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group...
