# Category

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**Category of being**— In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply categories. To investigate the categories of being is to determine the most fundamental and the broadest classes of entities.… …102

**Category of sets**— In mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose morphisms are all functions. It is the most basic and the most commonly used category in mathematics.Properties of the category of setsThe… …103

**Category of groups**— 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.The monomorphisms in Grp are precisely the… …104

**Category of manifolds**— In mathematics, the category of manifolds, often denoted Man p , is the category whose objects are manifolds of smoothness class C p and whose morphisms are p times continuously differentiable maps. This is a category because the composition of… …105

**Category of abelian groups**— In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category.The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the… …106

**Category 1 specialty channel**— A Category 1 specialty channel is a Canadian specialty television channel which, as defined by the Canadian Radio television and Telecommunications Commission, must be carried by all digital cable and direct broadcast satellite providers that… …107

**Category 2 specialty channel**— A Category 2 specialty channel is a Canadian specialty television channel which, as defined by the Canadian Radio television and Telecommunications Commission, may be carried, optionally, by all digital cable television and direct broadcast… …108

**Category of relations**— In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.A morphism (or arrow) R : A → B in this category is a relation between the sets A and B , so nowrap| R ⊆ A × B .The composition of two relations R …109

**Category of topological vector spaces**— In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear …110

**Category mistake**— A category mistake, or category error, is a semantic or ontological error by which a property is ascribed to a thing that could not possibly have that property. For example, the statement the business of the book sleeps eternally is syntactically …