Theorems · Theorem · category theory
CategoryTheory.Over.ConstructProducts.conesEquivInverse_map_hom
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (B : C) {J : Type w}
(F : CategoryTheory.Functor (CategoryTheory.Discrete J) (CategoryTheory.Over B)) {X Y : CategoryTheory.Limits.Cone F}
(f : X ⟶ Y),
((CategoryTheory.Over.ConstructProducts.conesEquivInverse B F).map f).hom = CategoryTheory.Over.Hom.left f.hom- Cited by
- 0 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites15
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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Limits.Conestatement and proof · cited by 710
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Over.Hom.leftstatement · cited by 287
- CategoryTheory.Limits.ConeMorphism.homstatement and proof · cited by 164
- CategoryTheory.Limits.WidePullbackShapestatement · cited by 94
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