Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

strengthen definition of limits/colimits #65

Open
TashiWalde opened this issue Sep 27, 2023 · 1 comment
Open

strengthen definition of limits/colimits #65

TashiWalde opened this issue Sep 27, 2023 · 1 comment

Comments

@TashiWalde
Copy link
Collaborator

TashiWalde commented Sep 27, 2023

In #50, limits are definined as terminal cones.

Implement an alternative (a priori stronger) characterization of limits:

  • Define cocone not as a single Sigma type, but as a type family cone : (f : A -> B) -> (b : B) -> U.
  • Define the canonical composition map cone-precomp b x : cone f x -> hom B b x -> cone f b.
  • Define limit (f : A->B) := Sigma ( x: X, c : cone f x ), (b : B) -> is-equiv (cone-precomp b x c)
  • Alternatively, if one wants to avoid inputting the composition map (which would require a Segal type),
    one could directly ask for an equivalence of dependent types (b:B) -> Equiv (hom B b x) (cone f b)
    and then show that for a Segal type this equivalence needs to be given by composition.
@cesarbm03
Copy link
Collaborator

Noted.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

No branches or pull requests

2 participants