Properties of functions: injective AKA 1:1, surjective AKA onto, bijective.
Functions have inverses iff they're 1:1 and onto.
If f,g are injective, so is g o f.
If g o f is injective, so is f (maybe not g).
Statement: every function X -> Y can be factored as a surjection X -> X/~, then a bijection X/~ -> S, then the inclusion of a subset S -> Y.
We'll prove it next time.
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