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.


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