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Theorems · Theorem · category theory

CategoryTheory.IsPullback.isIso_fst_of_mono

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y : C} {fst snd : P ⟶ X} {f : X ⟶ Y},
  CategoryTheory.IsPullback fst snd f f →
    autoParam (CategoryTheory.Mono f) CategoryTheory.IsPullback.isIso_fst_of_mono._auto_1 → CategoryTheory.IsIso fst
Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MorphismProperty.isIso_fst'_self · cited by 0MorphismProperty.isIso_fs…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Mono · cited by 893CategoryTheory.MonoCategoryTheory.IsPullback · cited by 320CategoryTheory.IsPullbackCategoryTheory.IsPullback.isLimit · cited by 47IsPullback.isLimitCategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimit · cited by 2PullbackCone.isIso_fst_of…IsPullback.isIso_fst_of_monoCITED BYCITES

Cites7

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Cited by1

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