Theorems · Theorem · category theory

CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape_of_isSuccLimit

∀ {J : Type w} {inst : LinearOrder J} {C : Type u} {inst_1 : CategoryTheory.Category.{v, u} C}
  [self : CategoryTheory.Limits.HasIterationOfShape J C] (j : J),
  Order.IsSuccLimit j → CategoryTheory.Limits.HasColimitsOfShape (↑(Set.Iio j)) C

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape
Cited by: 1 results in Mathlib
Foundations: Depth 17 from the axioms · uses propext
Assumes: CategoryTheory.Limits.HasIterationOfShape

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
CategoryTheory.Categorystatement and proof · cited by 32,673
LinearOrderstatement and proof · cited by 8,572
Set.Elemstatement · cited by 7,166
Set.Iiostatement · cited by 1,166
CategoryTheory.Limits.HasColimitsOfShapestatement · cited by 308
Order.IsSuccLimitstatement · cited by 255
CategoryTheory.Limits.HasIterationOfShapestatement and proof · cited by 58

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.hasColimitsOfShape_of_isSuccLimitproof · cited by 4