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Theorems · Definition · category theory

Bimod.TensorBimod.X

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [CategoryTheory.Limits.HasCoequalizers C] → {R S T : CategoryTheory.Mon C} → Bimod R S → Bimod S T → C

The underlying object of the tensor product of two bimodules.

Defined in
Mathlib.CategoryTheory.Monoidal.Bimod
Cited by
32 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasCoequalizers

Around this declaration

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

Bimod.tensorBimod · cited by 25Bimod.tensorBimodBimod.TensorBimod.actLeft · cited by 15TensorBimod.actLeftBimod.TensorBimod.actRight · cited by 14TensorBimod.actRightBimod.LeftUnitorBimod.hom · cited by 6LeftUnitorBimod.homBimod.RightUnitorBimod.hom · cited by 6RightUnitorBimod.homBimod.AssociatorBimod.hom_inv_id · cited by 5AssociatorBimod.hom_inv_idBimod.AssociatorBimod.hom_left_act_hom' · cited by 5AssociatorBimod.hom_left_…Bimod.AssociatorBimod.hom_right_act_hom' · cited by 5AssociatorBimod.hom_right…Bimod.AssociatorBimod.inv_hom_id · cited by 5AssociatorBimod.inv_hom_idBimod.LeftUnitorBimod.inv · cited by 4LeftUnitorBimod.invBimod.RightUnitorBimod.inv · cited by 4RightUnitorBimod.invBimod.TensorBimod.whiskerLeft_π_actLeft · cited by 4TensorBimod.whiskerLeft_π…Bimod.TensorBimod.π_tensor_id_actRight · cited by 4TensorBimod.π_tensor_id_a…Bimod.TensorBimod.actRight_one' · cited by 3TensorBimod.actRight_one'Bimod.TensorBimod.left_assoc' · cited by 3TensorBimod.left_assoc'CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.associator · cited by 667MonoidalCategoryStruct.as…CategoryTheory.Mon · cited by 465CategoryTheory.MonCategoryTheory.Mon.X · cited by 329Mon.XCategoryTheory.Limits.coequalizer · cited by 79Limits.coequalizerBimod · cited by 68BimodBimod.X · cited by 62Bimod.XCategoryTheory.Limits.HasCoequalizers · cited by 60Limits.HasCoequalizersBimod.actLeft · cited by 47Bimod.actLeftBimod.actRight · cited by 47Bimod.actRightTensorBimod.XCITED BYCITES

Cites15

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

Cited by39

Results whose statement or proof uses this declaration.