Discrete category

In the mathematical subfield of category theory a discrete category is a particularly trivial category. A category is said to be discrete if they only made ​​up of objects (and, if a distinction is made between, their identical morphisms ) is. Sometimes also be categories that are equivalent to such a category, are permitted. In some designs, discrete categories are an important special case. A category is then exactly discreet when it is at the same time and groupoid partial order.

Functors

Each mapping between two discrete categories is a functor. Thus can the category of sets to the category of ( small ) categories using a fully faithful functor embedding of any amount the discrete category, consisting of the elements of the set, assigns as objects.

Product Category

For a discrete (small ) category and any category is the category of functors from to with natural transformations as morphisms nothing more than the product category.

Products and coproducts

The product of a family of objects (if it exists) in a category is the special case of the general concept of limit: It's just the limit of the functor, where as a discrete category is conceived. Dually, the coproduct of that family of objects is (if it exists ) of the colimit functor this.