Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Over.braidedCategory

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] → (X : C) → CategoryTheory.BraidedCategory (CategoryTheory.Over X)

Over X is braided w.r.t. the Cartesian monoidal structure given by Limits.pullback.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Over
Cited by
16 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks
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Around this declaration

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

CategoryTheory.Over.η_pullback_left · cited by 1Over.η_pullback_leftCategoryTheory.Over.μ_pullback_left_fst_fst · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.Over.μ_pullback_left_fst_fst' · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.Over.μ_pullback_left_fst_snd · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.Over.μ_pullback_left_fst_snd' · cited by 1Over.μ_pullback_left_fst_…CategoryTheory.Over.μ_pullback_left_snd · cited by 1Over.μ_pullback_left_sndAlgebraicGeometry.Scheme.monObjAsOverPullback_mul · cited by 0Scheme.monObjAsOverPullba…AlgebraicGeometry.Scheme.monObjAsOverPullback_one · cited by 0Scheme.monObjAsOverPullba…CategoryTheory.Over.ε_pullback_left · cited by 0Over.ε_pullback_leftCategoryTheory.Over.μ_pullback_left_snd' · cited by 0Over.μ_pullback_left_snd'CategoryTheory.Over.monObjMkPullbackSnd_mul · cited by 0Over.monObjMkPullbackSnd_…CategoryTheory.Over.monObjMkPullbackSnd_one · cited by 0Over.monObjMkPullbackSnd_…CategoryTheory.Over.grpObjMkPullbackSnd_mul · cited by 0Over.grpObjMkPullbackSnd_…CategoryTheory.Over.grpObjMkPullbackSnd_one · cited by 0Over.grpObjMkPullbackSnd_…CategoryTheory.Over.braiding_hom_left · cited by 0Over.braiding_hom_leftCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.Over.cartesianMonoidalCategory · cited by 68Over.cartesianMonoidalCat…CategoryTheory.BraidedCategory.ofCartesianMonoidalCategory · cited by 0BraidedCategory.ofCartesi…Over.braidedCategoryCITED BYCITES

Cites6

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

Cited by16

Results whose statement or proof uses this declaration.