Theorems · Definition · category theory

CategoryTheory.Limits.BinaryFan.assocInv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      {sXY : CategoryTheory.Limits.BinaryFan X Y} →
        {sYZ : CategoryTheory.Limits.BinaryFan Y Z} →
          CategoryTheory.Limits.IsLimit sXY →
            CategoryTheory.Limits.BinaryFan X sYZ.pt → CategoryTheory.Limits.BinaryFan sXY.pt Z

Given binary fans sXY over X Y, and sYZ over Y Z, and s over X sYZ.X, if sYZ is a limit cone we can construct a binary fan over sXY.X Z. This is an ingredient of building the associator for a Cartesian category.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by: 6 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.pairstatement · cited by 536
CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
CategoryTheory.Limits.BinaryFan.sndproof · cited by 53
CategoryTheory.Limits.BinaryFan.fstproof · cited by 53
CategoryTheory.Limits.BinaryFanstatement and proof · cited by 51
CategoryTheory.Limits.BinaryFan.IsLimit.liftproof · cited by 12

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsLimit.assocproof · cited by 4
CategoryTheory.Over.associator_inv_left_fst_fstproof · cited by 1
CategoryTheory.Over.associator_inv_left_fst_sndproof · cited by 1
CategoryTheory.Over.associator_inv_left_sndproof · cited by 1
CategoryTheory.Limits.BinaryFan.assocInv_fststatement · cited by 0
CategoryTheory.Limits.BinaryFan.assocInv_sndstatement · cited by 0
CategoryTheory.Limits.IsLimit.assoc_liftstatement · cited by 0