Resumen
Un funtor covariante ∆ → A se llama objeto modelo de A, generando en A un enfoque similar a la topología algebraica cuando A es la categoría de espacios topológicos; este trabajo detalla los contextos y logros fundamentales del autor en relación a los objetos modelos.
Palabras clave
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[AM95] Marc Aubry, Homotopy Theory and Models, DMV Seminar B. 24, Birkhäuser Verlag, 1965.
[DFDJ] F. Bauer & J. Dugundji, Categorical Homotopy and Fibrations, Trans. Am. Math. Soc. 140 (1969), 239-256.
[CJ90] J. Cintura, Closed structures on reflective subcategories of the category of topological spaces, Theory and Appl of Categories 37 (1990), 237–247.
[DC56] C. H. Dowker, Homotopy extension theorems, Proc. London Math. Soc. 6 (3) (1956), 100–116.
[FR] R. Fritsch, On subdivisions of semisimplicial sets, Proc. of the International Symposium of Topology and Applications. Herceg-Novi (Yugoslavia), 25–31.8, 1968, 156–163.
[GPZM67] P. Gabriel & M. Zisman, Calculus on Fractions and Homotopy Theory, Springer–Verlag, Berlin, 1967.
[HK91] K. A. Hardie & K. H. Kamps, The coherent homotopy category over a fixed space is a category of fractions, Topology and its Applications 40 (1991), 265–274.
[HU59] S. T. Hu, Homotopy Theory, Academic Press, New York, 1959.
[JI84] I. James , General Topology and Homotopy Theory, Springer–Verlag, Heidelberg, 1984.
[KK] K. H. Kamps, Fibrations and cofibrations in categories with homotopy systems. Proc. of the International Symposium of Topology and Applications. Herceg-Novi (Yugoslavia), 25–31.8, 1968, 211–218.
[KK73] K. H. Kamps, Bemerkungen zum Homotopiesatz für semisimpliziale Faserungen, Bulletin de L'Académie Polonaise des Sciences 21 (4)1973.
[KK97] K. H. Kamps, Abstract Homotopy and simple homotopy theory, World Scientific, Singapore, 1997.
[KD58] Daniel Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294–329.
[KD55] Daniel Kan, Abstract Homotopy I, Proc. National Acad. Sciences 41 (1955), 1092–1096.
[KD561] Daniel Kan, Abstract Homotopy II, Proc. National Acad. Sciences 42 (1956), 225–228.
[KD562] Daniel Kan, Abstract Homotopy III, Proc. National Acad. Sciences 42 (1956), 419–421.
[KD57] Daniel Kan, On CSS complexes, Amer. J. Math. 79 (1957), 449–476.
[MJ90] Jean P. Mayer, Cosimplicial homotopies, Proc. Amer. Math. Soc. 108 (1990), 9–17.
[MP67] Peter May, Simplicial Objects in Algebraic Topology, D. van Nostrand, Princeton, 1967.
[MJ57] J. W. Milnor, The geometric realization of a semisimplicial complex, Ann. Math. 65 (1957), 357–362.
[OG89] Guillermo Ortiz, Modelos de homotopía, Tesis de Maestría, Universidad del Valle, Colombia, 1989.
[QD67] Daniel Quillen, Homotopical Algebra, Lectures Notes 43, Springer–Verlag, Berlin, 1967.
[RCLJ82] Carlos Ruiz & Joaquín Luna, Normalidad en realizaciones generalizadas (RY (X)), Collectanea Mathematica 33 (1982), 289–297.
[RCRR71] Carlos Ruiz & Roberto Ruiz–Salguero, La condición de Kan y la noción de grupoide, Rev. Colombiana Mat. 5 (1971), 59–82.
[RCRR73] Carlos Ruiz & Roberto Ruiz–Salguero, Kan fibrations which are homomorphisms of simplicial groups, Rev. Colombiana Mat. 7 (1973), 23–43.
[RCRR76] Carlos Ruiz & Roberto Ruiz–Salguero, Any equivalence relation over a category is a simplicial homotopy, Rev. Colombiana Mat. 10 (1976), 151–160.
[RCRR78] Carlos Ruiz & Roberto Ruiz–Salguero, Remarks about the Eilenberg–Zielber type decomposition in cosimplicial sets, Rev. Colombiana Mat. 12 (1978), 61–82.
[RCRR811] Carlos Ruiz & Roberto Ruiz–Salguero, Conditions over a realization functor to commute with finite products, Rev. Colombiana Mat. 15 (1971), 113–146.
[RCRR812] Carlos Ruiz & Roberto Ruiz–Salguero, Characterization of the set theoretical
geometric realization in the non Euclidean case, Proc. Amer. Math. Soc. 81 (1981), 321-324.
[RR] Roberto Ruiz–Salguero & Guillermo Ortiz, Levantamientos y homotopía abstracta, Lecturas Matemáticas 9 (1-3)(1988), 69-100.
[RR75] Roberto Ruiz–Salguero, Changes of Models in Algebraic Topology, Ph. D. Thesis, Temple University, 1975.
[RR77] Roberto Ruiz–Salguero, The closure of a model category, Rev. Colombiana Mat. 11 (1977), 19–50.
[RR79] Roberto Ruiz–Salguero, Subdivisiones relativas, Rev. Colombiana Mat. 13 (1979), 92–95.
[RR80] Roberto Ruiz–Salguero, Subdivisiones relativas sobre prehaces y homologías simpliciales isomorfas, Rev. Colombiana Mat. 14 (1980), 17–42.
[RR94] Roberto Ruiz–Salguero, Liftings in categorical homotopy, J. Pure Appl. Algebra 96 (1994), 157–172.
[VR73] R. M. Vogt, Homotopy limits and colimits, Math. Z. 134 (1973), 11–52.
[WH49] J. H. Whitehead, Combinatorial homotopy, Bull. Amer. Math. Soc. 55 (1949), 231–245.
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