Theorems · Theorem · category theory
CategoryTheory.Limits.multispanIndexCoend_left
∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {C : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} C]
(F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)) (f : (CategoryTheory.Limits.multispanShapeCoend J).L),
(CategoryTheory.Limits.multispanIndexCoend F).left f =
(F.obj (Opposite.op (CategoryTheory.Arrow.right f))).obj (CategoryTheory.Arrow.left f)- Defined in
- Mathlib.CategoryTheory.Limits.Shapes.End
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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 · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Arrow.leftstatement · cited by 426
- CategoryTheory.Arrow.rightstatement · cited by 423
- CategoryTheory.Limits.MultispanShape.Lstatement and proof · cited by 129
- CategoryTheory.Limits.MultispanIndex.leftstatement and proof · cited by 85
- CategoryTheory.Limits.multispanShapeCoendstatement and proof · cited by 19
- CategoryTheory.Limits.multispanIndexCoendstatement and proof · cited by 17
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