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Theorems · Theorem · category theory

CategoryTheory.SingleObj.id_as_one

∀ (M : Type u) [inst : Monoid M] (x : CategoryTheory.SingleObj M), CategoryTheory.CategoryStruct.id x = 1
Defined in
Mathlib.CategoryTheory.SingleObj
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
Monoid
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Around this declaration

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

CategoryTheory.SingleObj.inv_as_inv · cited by 3SingleObj.inv_as_invIsFreeGroupoid.SpanningTree.endIsFree · cited by 0SpanningTree.endIsFreeIsFreeGroupoid.path_nonempty_of_hom · cited by 0IsFreeGroupoid.path_nonem…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idMonoid · cited by 3887MonoidCategoryTheory.SingleObj · cited by 88CategoryTheory.SingleObjSingleObj.id_as_oneCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.