parallel morphisms

Two morphisms in a category CC are parallel if they have the same source and target. Equivalently a pair of parallel morphisms in CC consists of an object xx, and object yy, and two morphisms f,g:xyf, g: x \to y.

This can be extended to a family of any number of morphisms, but the morphisms are always compared pairwise to see if they are parallel. Degenerate cases: a family of one parallel morphism is simply a morphism; a family of zero parallel morphisms is simply a pair of objects.

The limit of a pair (or family) or morphisms is called their equalizer; the colimit is their coequalizer. (Of course, these do not always exist.)

Revised on January 29, 2011 22:04:45 by Toby Bartels (