Diagonal functor
In category theory , a branch of mathematics , the diagonal functor formula_1 is given by formula_2 , which maps objects as well as morphisms . 
<triplet> category theory <subj> objects <obj> studies <triplet> mathematics <subj> category theory <obj> has part <triplet> objects <subj> category theory <obj> studied by <subj> morphism <obj> has parts of the class <triplet> morphism <subj> category theory <obj> studied by <subj> objects <obj> part of