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Theorems · Theorem · category theory

CategoryTheory.Functor.Initial.hasLimitsOfShape_of_initial

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [F.Initial] {E : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} E]
  [CategoryTheory.Limits.HasLimitsOfShape C E], CategoryTheory.Limits.HasLimitsOfShape D E
Defined in
Mathlib.CategoryTheory.Limits.Final
Cited by
2 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.InitialCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShape
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CategoryTheory.CountableAB4Star.of_countableAB5Star · cited by 0CountableAB4Star.of_count…CategoryTheory.Limits.hasLimitsOfShape_of_initiallySmall · cited by 0Limits.hasLimitsOfShape_o…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Limits.HasLimitsOfShape · cited by 223Limits.HasLimitsOfShapeCategoryTheory.Functor.Initial · cited by 84Functor.InitialCategoryTheory.Functor.Initial.hasLimit_of_comp · cited by 2Initial.hasLimit_of_compInitial.hasLimitsOfShape_of_i…CITED BYCITES

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