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Theorems · Definition · algebraic topology

SSet.Subcomplex.unionProd.pushoutObjObj

{X Y : SSet} →
  (S : X.Subcomplex) → (T : Y.Subcomplex) → (CategoryTheory.MonoidalCategory.curriedTensor SSet).PushoutObjObj S.ι T.ι

Given subcomplexes S and T of simplicial sets, this if a Functor.PushoutObjObj structure for the chosen binary products on SSet, with point S.unionProd T.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.PushoutProduct
Cited by
10 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

SSet.Subcomplex.unionProd.pushoutObjObj_ι · cited by 2unionProd.pushoutObjObj_ιSSet.innerFibration_pullbackObjObjπ · cited by 1SSet.innerFibration_pullb…SSet.fibration_pullbackObjObjπ · cited by 1SSet.fibration_pullbackOb…SSet.Subcomplex.unionProd.pushoutObjObj_inl · cited by 0unionProd.pushoutObjObj_i…SSet.Subcomplex.unionProd.pushoutObjObj_inr · cited by 0unionProd.pushoutObjObj_i…SSet.Subcomplex.unionProd.pushoutObjObj_pt · cited by 0unionProd.pushoutObjObj_ptSSet.innerAnodyneExtensions_unionProd_ι · cited by 0SSet.innerAnodyneExtensio…SSet.anodyneExtensions_unionProd_ι · cited by 0SSet.anodyneExtensions_un…SSet.anodyneExtensions_unionProd_ι' · cited by 0SSet.anodyneExtensions_un…SSet.innerAnodyneExtensions_unionProd_ι' · cited by 0SSet.innerAnodyneExtensio…Opposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.Subcomplex · cited by 461SSet.SubcomplexSSet.Subcomplex.toSSet · cited by 315Subcomplex.toSSetCategoryTheory.MonoidalCategory.curriedTensor · cited by 170MonoidalCategory.curriedT…SSet.Subcomplex.ι · cited by 136Subcomplex.ιSSet.Subcomplex.unionProd · cited by 96Subcomplex.unionProdCategoryTheory.Functor.PushoutObjObj · cited by 54Functor.PushoutObjObjSSet.Subcomplex.unionProd.ι₁ · cited by 6unionProd.ι₁SSet.Subcomplex.unionProd.ι₂ · cited by 6unionProd.ι₂SSet.Subcomplex.unionProd.isPushout · cited by 2unionProd.isPushoutunionProd.pushoutObjObjCITED BYCITES

Cites12

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Cited by10

Results whose statement or proof uses this declaration.