Theorems · Definition · category theory

CategoryTheory.Limits.Fan.isLimitEquivOfEquiv

{β : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {γ : Type w'} →
        (ε : β ≃ γ) →
          {f : γ → C} →
            (c : CategoryTheory.Limits.Fan f) →
              CategoryTheory.Limits.IsLimit c ≃
                CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Fan.mk c.pt fun i => c.proj (ε i))

Being a limiting fan is stable under equivalences in the index type.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category