Theorems · Theorem · algebraic topology
FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone
∀ {I : Type u} (X : I → TopCat),
(FundamentalGroupoidFunctor.coneDiscreteComp X).functor.obj
(FundamentalGroupoid.fundamentalGroupoidFunctor.mapCone (TopCat.piFan X)) =
CategoryTheory.Limits.Fan.mk (FundamentalGroupoid.fundamentalGroupoidFunctor.obj (TopCat.of ((i : I) → ↑(X i))))
(FundamentalGroupoidFunctor.proj X)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- CategoryTheory.Functor.compstatement · cited by 6,529
- TopCat.carrierstatement · cited by 3,184
- CategoryTheory.Discretestatement · cited by 2,447
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Equivalence.functorstatement · cited by 1,268
- CategoryTheory.Limits.Conestatement · cited by 710
- CategoryTheory.Discrete.functorstatement · cited by 633
- CategoryTheory.Functor.mapConestatement · cited by 147
- CategoryTheory.Limits.Fan.mkstatement · cited by 46
- CategoryTheory.Grpdstatement · cited by 30
- FundamentalGroupoid.fundamentalGroupoidFunctorstatement · cited by 21
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