Homotopy for functors
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- by Ming Jung Lee PDF
- Proc. Amer. Math. Soc. 36 (1972), 571-577 Request permission
Erratum: Proc. Amer. Math. Soc. 42 (1974), 648-650.
Abstract:
We show that natural transformations play the role of homotopy for (covariant) functors. Homotopic functors are shown to induce identical maps between the homology groups of categories. For a space X, there is an associated category $\Lambda S(X)$. We show that the classifying space of $\Lambda S(X)$ has the same homotopy type as X if X is a CW complex. Moreover, we prove that, for CW complexes X and Y, f and $g:X \to Y$ are homotopic if and only if $\Lambda S(f)$ and $\Lambda S(g)$ are.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 571-577
- MSC: Primary 55J10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0334212-5
- MathSciNet review: 0334212