One well-knowncategory has sets as objects and functions as arrows.
Just as a monoidconsists of an underlyingset with a binary operation "on top of it" which is closed, associative and with an identity, a categoryconsists of an underlyingdigraph with an arrowcompositionoperation "on top of it" which is transitivelyclosed, associative, and with an identity at eachobject. In fact, a category's compositionoperation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.
Finally, in LC-MS/MS, the mostpopulatedcategorycorresponded to fatty acids (36%), followed byamino acids (22%), and sphingolipids and spingoid bases (21%).
If slicecategory C over X has twoobjects (A, f) and (B, g) and a morphism h : (A, f) → (B, g), then this morphism would correspond to a like-namedmorphism h : A → B of C such that .
“The datingindustry has come a longway since its inception, but the categoryremains underpenetrated.”