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Theorems · Definition · category theory

CategoryTheory.MonObj.ofIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {M X : C} → [CategoryTheory.MonObj M] → (M ≅ X) → CategoryTheory.MonObj X

Transfer MonObj along an isomorphism.

Defined in
Mathlib.CategoryTheory.Monoidal.Mon
Cited by
3 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonObj
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Around this declaration

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

CategoryTheory.GrpObj.ofIso · cited by 4GrpObj.ofIsoCategoryTheory.MonObj.ofIso_mul · cited by 2MonObj.ofIso_mulCategoryTheory.MonObj.ofIso_one · cited by 2MonObj.ofIso_oneCategoryTheory.Functor.essImage_mapMon · cited by 0Functor.essImage_mapMonCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.tensorHom · cited by 587MonoidalCategoryStruct.te…CategoryTheory.MonObj.mul · cited by 230MonObj.mulCategoryTheory.MonObj · cited by 199CategoryTheory.MonObjCategoryTheory.MonObj.one · cited by 189MonObj.oneMonObj.ofIsoCITED BYCITES

Cites10

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

Cited by4

Results whose statement or proof uses this declaration.