Editing Zero morphism (section)

==Related concepts==
If '''C''' has a zero object '''0''', given two objects ''X'' and ''Y'' in '''C''', there are canonical morphisms ''f'' : ''X'' → '''0''' and ''g'' : '''0''' → ''Y''. Then, ''gf'' is a zero morphism in Mor<sub>'''C'''</sub>(''X'', ''Y'').  Thus, every category with a zero object is a category with zero morphisms given by the composition 0<sub>''XY''</sub> : ''X'' → '''0''' → ''Y''.

If a category has zero morphisms, then one can define the notions of [[kernel (category theory)|kernel]] and [[cokernel]] for any morphism in that category.