# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 85: The Group as a Category

The group can be viewed as equivalent to a specific kind of category, specifically the category $C$ with only a single element and all of whose morphisms are isomorphisms. In this equivalence, the elements of the group correspond to the morphisms of $C$, the group operation to $\circ$ (composition), and the group identity to the identity morphism on the single element of $C$. Since all morphisms in $C$ are isomorphisms, each ‘element’ has an inverse, and $\circ$ is associative, analogous to the associativity of the group operation.