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Theorems · Theorem · category theory

CategoryTheory.AddMonObj.comp_add

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M X Y : C} [inst_2 : CategoryTheory.AddMonObj M] (f : X ⟶ Y) (g₁ g₂ : Y ⟶ M),
  CategoryTheory.CategoryStruct.comp f (g₁ + g₂) =
    CategoryTheory.CategoryStruct.comp f g₁ + CategoryTheory.CategoryStruct.comp f g₂
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by
9 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddMonObj

Around this declaration

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

CategoryTheory.AddGrpObj.lift_addCommutator_eq_add_add_neg_neg · cited by 2AddGrpObj.lift_addCommuta…CategoryTheory.AddGrpObj.lift_addConj_eq_add_add_neg · cited by 2AddGrpObj.lift_addConj_eq…CategoryTheory.AddMonObj.comp_nsmul · cited by 2AddMonObj.comp_nsmulCategoryTheory.AddGrpObj.whiskerLeft_η_addCommutator · cited by 1AddGrpObj.whiskerLeft_η_a…CategoryTheory.AddGrpObj.η_whiskerRight_addCommutator · cited by 1AddGrpObj.η_whiskerRight_…CategoryTheory.isCommAddMonObj_iff_isAddCommutative · cited by 1CategoryTheory.isCommAddM…CategoryTheory.IsAddMonHom.Normal.of_isPullback_η · cited by 0Normal.of_isPullback_ηCategoryTheory.IsAddMonHom.normal_iff_normal_addMonoidHom · cited by 0IsAddMonHom.normal_iff_no…CategoryTheory.AddMonObj.comp_add_assoc · cited by 0AddMonObj.comp_add_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.AddMonObj · cited by 158CategoryTheory.AddMonObjAddMonoidHom.map_add · cited by 48AddMonoidHom.map_addCategoryTheory.Hom.addMonoid · cited by 44Hom.addMonoidAddMonCat.Hom.hom · cited by 21Hom.homCategoryTheory.yonedaAddMon · cited by 8CategoryTheory.yonedaAddM…AddMonObj.comp_addCITED BYCITES

Cites12

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Cited by9

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