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Subcategory


Let C be a category. Then D is said to be a subcategory of C, if the objects of D are also objects of C, if the morphisms of D are also morphisms of C, and if D is a category in its own right. In particular, for each object X of D, the identity morphism id_X from C should also be in D, and compositions of morphisms in D should also be in D.

The functor denoted by I:D->C, the so-called inclusion functor which sends objects identically to objects, and morphisms identically to morphisms, is always a faithful functor.


See also

Category, Morphism

This entry contributed by Rasmus Hedegaard

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Cite this as:

Hedegaard, Rasmus. "Subcategory." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Subcategory.html

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