for all `s1`, `s2`, `s3` in `S`:
(i) `s1*s2` etc are also in `S`
(ii) `(s1*s2)*s3` = `s1*(s2*s3)`
+
+for all `s1`, `s2`, `s3` in `S`:
+(i) `s1*s2` etc are also in `S`
+(ii) `(s1*s2)*s3` = `s1*(s2*s3)`
(iii) `z*s1` = `s1` = `s1*z`

+
Some examples of monoids are:
@@ 60,8 +45,8 @@ When a morphism `f` in category **C** has source `C1` and target `C2`, we'll wri
To have a category, the elements and morphisms have to satisfy some constraints:
(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
+(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_{E}, which is such that for every morphism `f:C1>C2`: 1_{C2} o f = f = f o 1_{C1}