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Theorems · Theorem · category theory

CategoryTheory.Limits.prod.lift_snd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y : C}
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct X Y] (f : W ⟶ X) (g : W ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.lift f g) CategoryTheory.Limits.prod.snd = g
Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by
10 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProduct

Around this declaration

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

CategoryTheory.Limits.prodComparison_snd · cited by 5Limits.prodComparison_sndHomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…CategoryTheory.Limits.snd_opProdIsoCoprod_hom · cited by 2Limits.snd_opProdIsoCopro…CategoryTheory.Limits.preservesEqualizers_of_preservesPullbacks_and_binaryProducts · cited by 1Limits.preservesEqualizer…CategoryTheory.NonPreadditiveAbelian.lift_sub_lift · cited by 1NonPreadditiveAbelian.lif…HomotopicalAlgebra.RightHomotopyRel.postcomp · cited by 0RightHomotopyRel.postcompCategoryTheory.isSubterminal_of_isIso_diag · cited by 0CategoryTheory.isSubtermi…CategoryTheory.NormalMonoCategory.hasLimit_parallelPair · cited by 0NormalMonoCategory.hasLim…CategoryTheory.NormalMonoCategory.pullback_of_mono · cited by 0NormalMonoCategory.pullba…CategoryTheory.Limits.prod.lift_snd_assoc · cited by 0prod.lift_snd_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.prod · cited by 364Limits.prodCategoryTheory.Limits.limit.lift_π · cited by 266limit.lift_πCategoryTheory.Limits.prod.snd · cited by 185prod.sndCategoryTheory.Limits.HasBinaryProduct · cited by 169Limits.HasBinaryProductCategoryTheory.Limits.prod.lift · cited by 123prod.liftCategoryTheory.Limits.BinaryFan.mk · cited by 112BinaryFan.mkprod.lift_sndCITED BYCITES

Cites9

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Cited by10

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