Homotopy of Natural Transformations

Hardie, K. A.

Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 332-341

Résumé

Let C be a full subcategory of T, the category of based topological spaces and based maps, and let C n be the corresponding category of n-tuples. Let S, T: T n → T be covariant functors which respect homotopy classes and let u, v: S → T be natural transformations, u and v are homotopic inC, denoted u ≃ v(C), if uX ≃ vX: SX → TX (X ∈ C n ), that is to say, for every X ∈ C, uX and vX are homotopic (all homotopies are required to respect base points), u and v are naturally homotopic inC, denoted u ≃n v; (C), if there exist morphisms such that, for every X ∈ C, utX is a homotopy from uX to vX and such that, for every t ∈ I, ut :S → T is a natural transformation.

Détail

DOI : 10.4153/CJM-1970-041-2

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