## Algebraic topology: lectures, 1964-65, Parts 1-4 |

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adjoint adjoint functors admissible maps ALGEBRAIC TOPOLOGY axioms basepoint called cartesian product closed loop cocomposition cofibration cogroup compact compactly defined composition law Consider construct coproduct Corollary curve definition diagram commutes dual element epimorphism equivalence classes exact sequence Exercise fibration finite following diagram full subcategory functor G X A given group structure Hausdorff spaces Hence Hom-co-defined Hom-defined Properties hom(A homotopy extension Homotopy Extension Property homotopy sequence identity induced map injection inverse kernel Lemma Let f lifting map f mixed morphism monomorphism morphism in Q morphisms f natural transformation Note object in Q open cover open sets pair path pointed category product diagram projection Proof prop prove pullback diagram quasitopological spaces relative topology resp retraction Samuel Eilenberg set-theoretic simply strong pullback subsets topological spaces trivial map weak pullback weak pushout well-defined X X Y