Some results about path-cosplit maps #1167
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fredrik-bakke
commented
Aug 23, 2024
•
fredrik-bakke
commented
- When the domain is
$n+r+2$ -truncated the type of$n$ -path-cosplittings is$r$ -truncated - When the domain is
$n+1$ -truncated$n$ -path-cosplittings are unique - When the domain is
$n$ -truncated there are unique$n$ -path-cosplittings - path-cosplittings are closed under path-cosplit morphisms of arrows
- path-cosplittings are closed under equivalences of arrows
- path-cosplittings are closed under homotopies
- 3-for-2 of path-cosplittings
- products of path-cosplittings
- total space path-cosplittings
- dependent products of path-coplittings
- coproducts of path-cosplittings
So uhh, I felt a little inspired while reading Chris Grossack's blog post on [Finiteness in Sheaf Topoi](https://grossack.site/2024/08/19/finiteness-in-sheaf-topoi) this evening, and decided to have a look around and see if I could add any small definitions or external links to the library. Then things kind of derailed when I stumbled upon our file on pi-finite types. Turns out this file entangled three concepts (pi-finite types, locally finite types, and types with finite connected components). So I, uh..., unentangled it! 😬 I hope I'm not stepping on your toes, @EgbertRijke, I really did not intend to.
… is `r`-truncated
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