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.
Given a small category with set of objects and set of morphisms , the source function of is the function that maps each morphism in to its source object in .
Generalising this, given an internal category with object of objects and object of morphisms , the source morphism of is the morphism that is part of the definition of internal category.
Warning: there is another meaning of ‘source’ in category theory; see sink.