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Good #Beer #duvel #belgium #finset (at Circuit Zolder)

#duvel #belgium #finset #beer

what is it about the binary coproducts of finite sets that makes A+B = A+C imply B = C? (note: “=“ means “is isomorphic to” in this post)

it’s easy to see that this isn’t the case for general coproducts, and indeed this isn’t even true for infinite sets, since strict inequalities of infinite sets A>B>C imply A+B = A+C = A (maybe you need choice for that?)

so apparently the property of interest isn’t a consequence of FinSet being a topos, nor the fact that its coproducts are freely generated

what’s so special about coproducts in FinSet, and where else does A+B = A+C imply B = C?

#category theory #coproducts #FinSet #mathema #own

so apparently just as the cat of finite sets is the free cat-with-finite-coproducts generated by 1 (the set with one element), its opposite, the cat of finite boolean algebras, is the free cat-with-finite-products generated by 1 (the powerset of the empty set)

(see Proposition 1 here)

#category theory #finset #finbool #own #text #mathema