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Theorems · Theorem · algebraic topology

FundamentalGroup.map_apply

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (f : C(X, Y)) (x : X)
  (a : { as := x } ⟶ { as := x }), (FundamentalGroup.map f x) a = Path.Homotopic.Quotient.map a f
Defined in
Mathlib.AlgebraicTopology.FundamentalGroupoid.FundamentalGroup
Cited by
1 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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IsCoveringMap.existsUnique_continuousMap_lifts_of_range_le · cited by 0IsCoveringMap.existsUniqu…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomTopologicalSpace · cited by 24529TopologicalSpaceCategoryTheory.Functor.obj · cited by 19642Functor.objMonoidHom · cited by 3629MonoidHomContinuousMap · cited by 2491ContinuousMapFundamentalGroupoid · cited by 60FundamentalGroupoidFundamentalGroup · cited by 30FundamentalGroupPath.Homotopic.Quotient.map · cited by 19Quotient.mapFundamentalGroupoid.map · cited by 6FundamentalGroupoid.mapFundamentalGroup.map · cited by 2FundamentalGroup.mapFundamentalGroup.map_applyCITED BYCITES

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