Theorems · Inductive type · category theory
Opposite
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The type of objects of the opposite of α; used to define the opposite category.
Now that Lean 4 supports definitional eta equality for records,
both unop (op X) = X and op (unop X) = X are definitional equalities.
- Defined in
- Mathlib.Data.Opposite
- Cited by
- 8,081 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by11,303
Results whose statement or proof uses this declaration.
- Opposite.unopstatement and proof · cited by 2,231
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.Functor.opstatement and proof · cited by 997
- CategoryTheory.Presheaf.IsSheafstatement and proof · cited by 991
- Quiver.Hom.unopstatement and proof · cited by 903
- CategoryTheory.SimplicialObjectproof · cited by 548
- SSet.stdSimplexstatement · cited by 499
- TopCat.Presheafproof · cited by 371
- CategoryTheory.yonedastatement and proof · cited by 351
- PresheafOfModulesstatement · cited by 247
- CategoryTheory.Functor.rightOpstatement and proof · cited by 214
- CategoryTheory.coyonedastatement · cited by 208
Showing the 200 most cited of 11,303.