Discrete category
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In category theory, a discrete category is a category whose only morphisms are the identity morphisms. It is the simplest kind of category. Specifically a category C is discrete if
- MorC(X, X) = {idX} for all objects X
- MorC(X, Y) = ∅ for all objects X ≠ Y
Clearly, any class of objects defines a discrete category when augmented with identity maps.
Any subcategory of a discrete category is discrete.
The limit of any functor from a discrete category into another category is called a product, while the colimit is called a coproduct.