Science Fair Project Encyclopedia
Discrete category
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.
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details