Topic summary
surjective
Extracted from the Wikipedia article Surjective function.
Composition and decomposition
The composition of surjective functions is always surjective: If f and g are both surjective, and the codomain of g is equal to the domain of f, then fog is surjective. Conversely, if fog is surjective, then f is surjective (but g, the function applied first, need not be). These properties generalize from surjections in the category of sets to any epimorphisms in any category.