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Theorems · Theorem · category theory

CategoryTheory.Preadditive.hasWeakEqualizer_of_hasWeakKernel

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C}
  (f g : X ⟶ Y) [CategoryTheory.Limits.HasWeakKernel (f - g)], CategoryTheory.Limits.HasWeakEqualizer f g

A preadditive category has a weak equalizer for f and g if it has a weak kernel for f - g.

Defined in
Mathlib.CategoryTheory.Limits.WeakLimits.WeakKernels
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasWeakKernel
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CategoryTheory.Preadditive.hasWeakEqualizers_of_hasWeakKernels · cited by 0Preadditive.hasWeakEquali…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Limits.Fork.ofι · cited by 66Fork.ofιCategoryTheory.Limits.HasWeakEqualizer · cited by 10Limits.HasWeakEqualizerCategoryTheory.Limits.weakEqualizer.ι · cited by 9weakEqualizer.ιCategoryTheory.Preadditive.forkOfKernelFork · cited by 8Preadditive.forkOfKernelF…CategoryTheory.Limits.HasWeakKernel · cited by 8Limits.HasWeakKernelCategoryTheory.Limits.HasWeakLimit.mk · cited by 4HasWeakLimit.mkCategoryTheory.Limits.weakEqualizer.condition · cited by 3weakEqualizer.conditionCategoryTheory.Preadditive.isWeakLimitForkOfKernelFork · cited by 2Preadditive.isWeakLimitFo…CategoryTheory.Limits.weakEqualizerIsWeakEqualizer · cited by 1Limits.weakEqualizerIsWea…Preadditive.hasWeakEqualizer_…CITED BYCITES

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