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Theorems · Inductive type · category theory

CategoryTheory.ExactPairing

{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → [CategoryTheory.MonoidalCategory C] → C → C → Type v₁

An exact pairing is a pair of objects X Y : C which admit a coevaluation and evaluation morphism which fulfill two triangle equalities.

Defined in
Mathlib.CategoryTheory.Monoidal.Rigid.Basic
Cited by
20 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.ExactPairing.coevaluation · cited by 29ExactPairing.coevaluationCategoryTheory.ExactPairing.evaluation · cited by 29ExactPairing.evaluationCategoryTheory.tensorLeftHomEquiv · cited by 9CategoryTheory.tensorLeft…CategoryTheory.tensorRightHomEquiv · cited by 9CategoryTheory.tensorRigh…CategoryTheory.ExactPairing.coevaluation_evaluation'' · cited by 3ExactPairing.coevaluation…CategoryTheory.ExactPairing.evaluation_coevaluation'' · cited by 3ExactPairing.evaluation_c…CategoryTheory.ExactPairing.coevaluation' · cited by 2ExactPairing.coevaluation'CategoryTheory.ExactPairing.coevaluation_evaluation · cited by 2ExactPairing.coevaluation…CategoryTheory.ExactPairing.evaluation' · cited by 2ExactPairing.evaluation'CategoryTheory.ExactPairing.evaluation_coevaluation · cited by 2ExactPairing.evaluation_c…CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft · cited by 1CategoryTheory.tensorLeft…CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight · cited by 1CategoryTheory.tensorRigh…CategoryTheory.ExactPairing.coevaluation_evaluation' · cited by 1ExactPairing.coevaluation…CategoryTheory.ExactPairing.coevaluation_evaluation_assoc · cited by 1ExactPairing.coevaluation…CategoryTheory.ExactPairing.evaluation_coevaluation' · cited by 1ExactPairing.evaluation_c…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.ExactPairingCITED BYCITES

Cites2

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Cited by52

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