Against the Category Theorists

A category is

a collection of objects

a collection of pairwise morphisms between objects in the collection

Compositions of morphisms can be constructed such that if f o A->B and g o B->C, then f o g A->C

Laws of categories

Morphism compositions are associative, such that (f o g) o h = f o (g o h)

Secondly, the category needs to be closed under the composition operation. So if {\displaystyle f:B\to C} and {\displaystyle g:A\to B}, then there must be some morphism {\displaystyle h:A\to C} in the category such that {\displaystyle h=f\circ g}. 

There exists an identity morphism

There exist constructs that are both categories and objects, for example the holon.

Any time a multi-way relationship exists, i.e. a morphism