Skip to content

Add the category of sets with finite-to-one maps#117

Open
ScriptRaccoon wants to merge 3 commits intomainfrom
finite-to-one-maps
Open

Add the category of sets with finite-to-one maps#117
ScriptRaccoon wants to merge 3 commits intomainfrom
finite-to-one-maps

Conversation

@ScriptRaccoon
Copy link
Copy Markdown
Owner

@ScriptRaccoon ScriptRaccoon commented Apr 20, 2026

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).

@ScriptRaccoon ScriptRaccoon linked an issue Apr 20, 2026 that may be closed by this pull request
@ScriptRaccoon ScriptRaccoon marked this pull request as ready for review April 20, 2026 21:13
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

Projects

None yet

Development

Successfully merging this pull request may close these issues.

Category of sets where maps have finite fibers

1 participant