This entry is about the basic notion of “source” in category theory. For another use in category theory see at sink and for the use in physics see at source field. There is also source forms in variational calculus.



The source object, or simply source, of a morphism f:xyf: x \to y in some category CC is the object xx. The source of ff is also called its domain, although that can be confusing in categories of partial functions.

Given a small category CC with set of objects C 0C_0 and set of morphisms C 1C_1, the source function of CC is the function s:C 1C 0s: C_1 \to C_0 that maps each morphism in C 1C_1 to its source object in C 0C_0.

Generalising this, given an internal category CC with object of objects C 0C_0 and object of morphisms C 1C_1, the source morphism of CC is the morphism s:C 1C 0s: C_1 \to C_0 that is part of the definition of internal category.

Warning: there is another meaning of ‘source’ in category theory; see sink.

Last revised on August 26, 2015 at 03:01:28. See the history of this page for a list of all contributions to it.