Theorems · Theorem · category theory
CategoryTheory.Functor.IsRepresentedBy.representableBy.congr_simp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
{x x_1 : F.obj (Opposite.op X)} (e_x : x = x_1) (h : F.IsRepresentedBy x), h.representableBy = ⋯.representableBy- Defined in
- Mathlib.CategoryTheory.RepresentedBy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.RepresentableBystatement · cited by 51
- CategoryTheory.Functor.IsRepresentedBystatement and proof · cited by 14
- CategoryTheory.Functor.IsRepresentedBy.representableBystatement and proof · cited by 6
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