Theorems · Theorem · category theory

CategoryTheory.StructuredArrow.projectSubobject_mk

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {S : D} {T : CategoryTheory.Functor C D} [inst_2 : CategoryTheory.Limits.HasFiniteLimits C]
  [inst_3 : CategoryTheory.Limits.PreservesFiniteLimits T] {A P : CategoryTheory.StructuredArrow S T} (f : P ⟶ A)
  [inst_4 : CategoryTheory.Mono f],
  CategoryTheory.StructuredArrow.projectSubobject (CategoryTheory.Subobject.mk f) =
    CategoryTheory.Subobject.mk (CategoryTheory.StructuredArrow.Hom.right f)

Defined in: Mathlib.CategoryTheory.Subobject.Comma
Cited by: 0 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasFiniteLimits CategoryTheory.Limits.PreservesFiniteLimits CategoryTheory.Mono

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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.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Monostatement and proof · cited by 893
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Subobjectstatement · cited by 385
CategoryTheory.StructuredArrowstatement and proof · cited by 370
CategoryTheory.StructuredArrow.rightstatement · cited by 213
CategoryTheory.Limits.PreservesFiniteLimitsstatement and proof · cited by 121
CategoryTheory.Subobject.mkstatement · cited by 109
CategoryTheory.StructuredArrow.Hom.rightstatement · cited by 82

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