Non functorial cylinders in a model category

• Autorzy: J. García-Calcines , P. García-Díaz , S. Rodríguez-Machín
• Języki publikacji: EN

Abstrakty

EN

Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids.

Słowa kluczowe

EN

Model category; cofibration category; cylinder object; homotopy groupoid; 55U35; 55P05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 3
• Strony: 376-394

Daty

wydano

2006-09-01

online

2006-09-01

Twórcy

autor

J. García-Calcines

• University of La Laguna,

autor

P. García-Díaz

• University of La Laguna

autor

S. Rodríguez-Machín

• University of La Laguna

Bibliografia

• [1] M. Artin and B. Mazur: Etale homotopy, Lecture Notes in Maths, Vol. 100, Springer-Verlag, 1969.
• [2] H.J. Baues: Algebraic homotopy, Cambridge University Press, 1989.
• [3] D.A. Edwards and H.M. Hastings: Cech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, Vol. 542, Springer Verlag, 1976.
• [4] K. Hess: “Model categories in algebraic topology,” Appl. Categ. Struct., Vol. 10(3), (2002), pp. 195–220. http://dx.doi.org/10.1023/A:1015218106586
• [5] P.S. Hirschhorn: Model Categories and Their Localizations, Mathematical Surveys and Monographs, Vol. 99, Amer. Math. Soc, 2003.
• [6] M. Hovey: Model Categories, Mathematical Surveys and Monographs, Vol. 63, Amer. Math. Soc, 1999.
• [7] D.C. Isaksen: “Strict model structures for pro-categories, Categorical decomposition techniques in algebraic topology”, Prog. Math., Vol. 215, (2004), pp. 179–198.
• [8] D.G. Quillen: Homolopical Algebra, Lecture Notes in Maths, Vol. 43, Springer-Verlag, 1967.

Identyfikatory

DOI

10.2478/s11533-006-0021-x