- (i) the class of morphisms has to be closed under composition: where f:C1->C2 and g:C2->C3, g o f is also a morphism of the category, which maps C1->C3.
- (ii) composition of morphisms has to be associative
- (iii) every element e of the category has to have an identity morphism id[e], which is such that for every morphism f:C1->C2: id[C2] o f = f = f o id[C1]
+<blockquote><pre>
+(i) the class of morphisms has to be closed under composition: where `f:C1->C2` and `g:C2->C3`, `g o f` is also a morphism of the category, which maps `C1->C3`.
+(ii) composition of morphisms has to be associative
+(iii) every element `E` of the category has to have an identity morphism 1<sub>E</sub>, which is such that for every morphism `f:C1->C2`: 1<sub>C2</sub> o f = f = f o 1<sub>C1</sub>
+</pre></blockquote>