Theorems · Definition · category theory
CategoryTheory.ihom.ev
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
(A : C) →
[inst_2 : CategoryTheory.Closed A] →
(CategoryTheory.ihom A).comp (CategoryTheory.MonoidalCategory.tensorLeft A) ⟶ CategoryTheory.Functor.id CThe evaluation natural transformation.
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Adjunction.counitproof · cited by 376
- CategoryTheory.ihomstatement · cited by 179
- CategoryTheory.MonoidalCategory.tensorLeftstatement · cited by 170
- CategoryTheory.Closedstatement and proof · cited by 90
- CategoryTheory.ihom.adjunctionproof · cited by 31
Cited by43
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalClosed.uncurry_eqstatement · cited by 9
- CategoryTheory.MonoidalClosed.compTransposeproof · cited by 7
- CategoryTheory.MonoidalClosed.ihomCurryproof · cited by 7
- CategoryTheory.MonoidalClosed.ihomUncurryproof · cited by 6
- CategoryTheory.MonoidalClosed.uncurry_id_eq_evstatement and proof · cited by 6
- CategoryTheory.MonoidalClosed.compTranspose_eqstatement · cited by 4
- CategoryTheory.ihom.ev_naturalitystatement and proof · cited by 4
- CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_evstatement · cited by 3
- CategoryTheory.Functor.closedCounitproof · cited by 3
- CategoryTheory.MonoidalClosed.whiskerLeft_curry'_compproof · cited by 3
- CategoryTheory.MonoidalClosed.whiskerLeft_curry'_ihom_ev_appstatement · cited by 3
- CategoryTheory.MonoidalClosed.whiskerLeft_curry_ihom_ev_appstatement and proof · cited by 3