Theorems · Definition · category theory

CategoryTheory.InducedCategory.homEquiv

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v, u₂} D] →
      {F : C → D} → {X Y : CategoryTheory.InducedCategory D F} → (X ⟶ Y) ≃ (F X ⟶ F Y)

Morphisms in InducedCategory D F identify to morphisms in D.

Defined in: Mathlib.CategoryTheory.InducedCategory
Cited by: 2 results in Mathlib
Foundations: Depth 13 from the axioms · uses propext
Assumes: CategoryTheory.Category

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Cites6

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
Equivstatement · cited by 8,337
CategoryTheory.InducedCategory.Hom.homproof · cited by 850
CategoryTheory.InducedCategorystatement and proof · cited by 71
CategoryTheory.InducedCategory.homMkproof · cited by 33

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.InducedCategory.endEquivproof · cited by 5
CategoryTheory.InducedCategory.homAddEquivproof · cited by 2
CategoryTheory.InducedCategory.homEquiv_applystatement and proof · cited by 0
CategoryTheory.InducedCategory.homEquiv_symm_apply_homstatement and proof · cited by 0