Theorems · Theorem · category theory
CategoryTheory.Over.sections_obj
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
(I : C) [inst_2 : CategoryTheory.Closed I]
[inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.curryRightUnitorHom I)] (X : CategoryTheory.Over I),
(CategoryTheory.Over.sections I).obj X =
CategoryTheory.ChosenPullbacksAlong.pullbackObj ((CategoryTheory.ihom I).map X.hom)
(CategoryTheory.curryRightUnitorHom I)- Cited by
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- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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.Functor.mapstatement · cited by 8,698
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Over.homstatement · cited by 370
- CategoryTheory.ihomstatement · cited by 179
- CategoryTheory.Closedstatement and proof · cited by 90
- CategoryTheory.ChosenPullbacksAlongstatement and proof · cited by 73
- CategoryTheory.ChosenPullbacksAlong.pullbackObjstatement · cited by 42
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