Theorems · Definition · algebraic topology
SSet.stdSimplex.opObjEquiv
{n : SimplexCategory} → {d : SimplexCategoryᵒᵖ} → (SSet.stdSimplex.obj n).op.obj d ≃ (SSet.stdSimplex.obj n).obj dThe bijection (stdSimplex.obj n).op.obj d ≃ (stdSimplex.obj n).obj d for any
n : ℕ and d : ℕ. See also stdSimplex.opIso.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement and proof · cited by 8,081
- Equiv.symmproof · cited by 3,681
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- Equiv.transproof · cited by 337
- SSet.stdSimplex.objEquivproof · cited by 59
- SSet.opstatement · cited by 33
- CategoryTheory.Functor.FullyFaithful.homEquivproof · cited by 31
- SSet.opObjEquivproof · cited by 26
Cited by7
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.opIsoproof · cited by 4
- SSet.stdSimplex.opIso_inv_app_hom_applystatement · cited by 2
- SSet.op_hornproof · cited by 0
- SSet.op_boundaryproof · cited by 0
- SSet.stdSimplex.opIso_hom_app_hom_applystatement · cited by 0
- SSet.stdSimplex.opObjEquiv_applystatement · cited by 0
- SSet.stdSimplex.opObjEquiv_opObjEquiv_symm_applystatement · cited by 0