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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Homotopy for functors

Author: Ming Jung Lee
Journal: Proc. Amer. Math. Soc. 36 (1972), 571-577
MSC: Primary 55J10
Erratum: Proc. Amer. Math. Soc. 42 (1974), 648-650.
MathSciNet review: 0334212
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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 [Enhancements On Off] (What's this?)

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PII: S 0002-9939(1972)0334212-5
Keywords: Small category, simplicial set, homotopy, subdivision, morphism complex, classifying space
Article copyright: © Copyright 1972 American Mathematical Society