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Theorems · Definition · category theory

CategoryTheory.WithTerminal.opEquiv

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] → (CategoryTheory.WithTerminal C)ᵒᵖ ≌ CategoryTheory.WithInitial Cᵒᵖ

The opposite category of WithTerminal C is equivalent to WithInitial Cᵒᵖ.

Defined in
Mathlib.CategoryTheory.WithTerminal.Basic
Cited by
8 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app · cited by 0WithTerminal.opEquiv_coun…CategoryTheory.WithTerminal.opEquiv_counitIso_inv_app · cited by 0WithTerminal.opEquiv_coun…CategoryTheory.WithTerminal.opEquiv_functor_map · cited by 0WithTerminal.opEquiv_func…CategoryTheory.WithTerminal.opEquiv_functor_obj · cited by 0WithTerminal.opEquiv_func…CategoryTheory.WithTerminal.opEquiv_inverse_map · cited by 0WithTerminal.opEquiv_inve…CategoryTheory.WithTerminal.opEquiv_inverse_obj · cited by 0WithTerminal.opEquiv_inve…CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app · cited by 0WithTerminal.opEquiv_unit…CategoryTheory.WithTerminal.opEquiv_unitIso_inv_app · cited by 0WithTerminal.opEquiv_unit…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Functor.id · cited by 3333Functor.idOpposite.unop · cited by 2231Opposite.unopQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.NatIso.ofComponents · cited by 178NatIso.ofComponentsCategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.WithInitial · cited by 144CategoryTheory.WithInitialWithTerminal.opEquivCITED BYCITES

Cites21

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Cited by8

Results whose statement or proof uses this declaration.