Theorems · Definition · algebraic topology
SSet.opObjEquiv
{X : SSet} → {n : SimplexCategoryᵒᵖ} → X.op.obj n ≃ X.obj nThe type of n-simplices of X.op identify to type of n-simplices of X.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement and proof · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement and proof · cited by 1,283
- Equiv.reflproof · cited by 274
- SSet.opstatement and proof · cited by 33
Cited by35
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.opObjEquivproof · cited by 6
- SSet.N.opEquivproof · cited by 4
- SSet.opFunctorCompOpFunctorIsoproof · cited by 4
- SSet.S.opEquivproof · cited by 3
- SSet.op_δstatement and proof · cited by 2
- SSet.PtSimplex.opstatement · cited by 2
- SSet.PtSimplex.opEquivstatement and proof · cited by 2
- SSet.PtSimplex.MulStruct.opstatement and proof · cited by 1
- SSet.PtSimplex.MulStruct.unopstatement and proof · cited by 1
- SSet.S.opEquiv_symm_applystatement · cited by 1
- SSet.op_σstatement and proof · cited by 1
- SSet.PtSimplex.opEquiv_apply_mapstatement and proof · cited by 0