Limits and colimits indexed by preorders #
In this file, we obtain the following very basic results
about limits and colimits indexed by a preordered type J
:
- a least element in
J
implies the existence of all limits indexed byJ
- a greatest element in
J
implies the existence of all colimits indexed byJ
instance
Preorder.instHasLimitsOfShape
(J : Type w)
[Preorder J]
(C : Type u)
[CategoryTheory.Category.{v, u} C]
[OrderBot J]
:
instance
Preorder.instHasColimitsOfShape
(J : Type w)
[Preorder J]
(C : Type u)
[CategoryTheory.Category.{v, u} C]
[OrderTop J]
: