[keithalewis]

Category theory is just another way of looking at math besides the impoverished notion "everything is a set". Mathematics is used in computer science. Rust is a great example. Jean-Yves Girard invented linear logic to make Gerhard Gentzen's sequent calculus symmetric, similar to Paul Dirac's theory that led to the discovery of positrons. Girard's concern about using a proposition exactly once in a proof led to borrow checking.

Putting on category theory glasses can help discover and clarify new facts. Thinking in terms of objects and arrows leads to duality: reverse the direction of the arrows.

The category Set is only one of many categories. The objects are sets and the arrows are functions. A function I -> S that is 1-1/injective/mono[1] corresponds to the set theory notion of a "subset". The dual is a function S -> I that is onto/surjective/epi[2]. What set theory notion does this correspond to?

Hint: Look into David Ellerman. He is the von Neumann of our times.

[1] f is mono if fg = fh implies g = h. [2] f is epi if gf = hf implies g = h.

Hi Dang.