Homotopy limits and the homotopy type of functor categories
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- by David A. Cox PDF
- Proc. Amer. Math. Soc. 58 (1976), 55-58 Request permission
Abstract:
Let ${\mathbf {Y}}:I \to$ Simplicial Sets be a functor. We give a sufficient condition for the map ${\text {ho}}\lim \limits _ \to {\mathbf {Y}} \to \lim \limits _ \to {\mathbf {Y}}$ to be a weak equivalence. Then we apply this to determine the Artin-Mazur homotopy type of the functor category Funct($I$, Sets).References
- Théorie des topos et cohomologie étale des schémas. Tome 2, Lecture Notes in Mathematics, Vol. 270, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. MR 0354653
- M. Artin and B. Mazur, Etale homotopy, Lecture Notes in Mathematics, No. 100, Springer-Verlag, Berlin-New York, 1969. MR 0245577
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 55-58
- MSC: Primary 14F35; Secondary 18A25
- DOI: https://doi.org/10.1090/S0002-9939-1976-0407022-1
- MathSciNet review: 0407022