Wed Jan 17

Recall: group = a set + three operations + some axioms. Group homomorphism: a function preserving the operations.
Recall: category = two sets (objects and morphisms) + two operations + some axioms. Define a functor as two functions preserving the operations.

Some examples:
Forgetful functors (-> Set).
The vector space with given basis (Set -> Vec).
The one-object category made from a group (Grp -> Cat, G |-> C_G).
G-sets (C_G -> Set).

Natural transformations of functors.