Add the category of sets with finite-to-one maps#117
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ScriptRaccoon wants to merge 3 commits intomainfrom
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Add the category of sets with finite-to-one maps#117ScriptRaccoon wants to merge 3 commits intomainfrom
ScriptRaccoon wants to merge 3 commits intomainfrom
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This PR adds the category$Set_f$ to the database, whose objects are sets and whose morphisms are maps whose fibers are finite (also called finite-to-one maps). I had asked about this category in MSE/5012262.
This category has some interesting properties. It is extensive, locally (!) cartesian closed,$\aleph_1$ -accessible (!), and it has equalizers. It does not have finite products, countable coproducts, or coequalizers. All properties except for one have been decided: coaccessible, cf. #91.
TODO: wait for merge of #115, then decide if the category has quotients (or coquotients).