Theorems · Theorem · category theory

CategoryTheory.Limits.hasLimit_of_closedUnderLimits

∀ (J : Type w) [inst : CategoryTheory.Category.{w', w} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  (P : CategoryTheory.ObjectProperty C) [P.IsClosedUnderLimitsOfShape J]
  (F : CategoryTheory.Functor J P.FullSubcategory) [CategoryTheory.Limits.HasLimit (F.comp P.ι)],
  CategoryTheory.Limits.HasLimit F

Defined in: Mathlib.CategoryTheory.Limits.FullSubcategory
Cited by: 0 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape CategoryTheory.Limits.HasLimit

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.ObjectProperty.FullSubcategorystatement and proof · cited by 726
CategoryTheory.Limits.HasLimitstatement and proof · cited by 226
CategoryTheory.ObjectProperty.ιstatement and proof · cited by 95
CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShapestatement and proof · cited by 49
CategoryTheory.hasLimit_of_createdproof · cited by 9
CategoryTheory.CreatesLimitproof · cited by 6
CategoryTheory.Limits.createsLimitFullSubcategoryInclusionOfClosedproof · cited by 1

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