Theorems · Theorem · category theory
CategoryTheory.MonObj.one_eq_one
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
(M : C) [inst_2 : CategoryTheory.MonObj M], CategoryTheory.MonObj.one = 1- Cited by
- 5 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonObjstatement and proof · cited by 199
- CategoryTheory.MonObj.onestatement and proof · cited by 189
- CategoryTheory.SemiCartesianMonoidalCategory.toUnitproof · cited by 103
- CategoryTheory.Hom.monoidstatement · cited by 52
- CategoryTheory.SemiCartesianMonoidalCategory.toUnit_uniqueproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.η_whiskerRight_commutatorproof · cited by 2
- CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_ηproof · cited by 2
- CategoryTheory.GrpObj.whiskerLeft_η_commutatorproof · cited by 2
- CategoryTheory.GrpObj.one_invproof · cited by 1
- AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegralproof · cited by 0