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Abstract:

We show how to construct a categorical spectrum of small categories, and hence a cohomology theory, starting from a Γ-category. This extends Segal's infinite loop space machine for topological spaces to small categories. Our results form a part of Bak's program for delooping global actions, global categories, and related objects. © Springer Science+Business Media B.V. 2006.

Registro:

Documento: Artículo
Título:Spectra of small categories and infinite loop space machines
Autor:Minian, E.G.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Infinite loop spaces; Simplicial objects; Small categories
Año:2006
Volumen:37
Número:3
Página de inicio:249
Página de fin:261
DOI: http://dx.doi.org/10.1007/s10977-006-0017-0
Título revista:K-Theory
Título revista abreviado:K-Theory
ISSN:09203036
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09203036_v37_n3_p249_Minian

Referencias:

  • Bousfield, A.K., Friedlander, E.M., Homotopy theory of T-spaces, spectra and bisimplicial sets (1978) Lect. Notes Math., 658, pp. 80-130
  • Torn Dieck, T., Kamps, K.H., Puppe, D., Homotopietheorie (1970) Lect. Notes Math., 157, pp. vi+265p
  • Dold, A., Partitions of unity in the theory of fibrations (1963) Ann. Math., 78, pp. 223-255
  • Fritsch, R., Piccinini, R.A., Cellular structures in topology (1990) Cambridge Stud. Adv. Math., 19, pp. XII+326p
  • Hoff, G., Catégories fibrées et homotopie (1974) C.R. Acad. Sci. Paris, 278, pp. 223-225
  • Hoff, G., Introduction à l'homotopie dans Cat (1975) Esquisses Mathématiques, 23, pp. i+33p
  • Lee, M.J., Homotopy for functors (1972) Proc. Amer. Math. Soc., 36, pp. 571-577
  • May, P., Thomason, R., The uniqueness of infinite loop space machines (1978) Topology, 17, pp. 205-224
  • Minian, E.G., Cat as a Lambda-cofibration category (2002) J. Pure Appl. Algebra, 167, pp. 301-314
  • Minian, E.G., Complexes in cat (2002) Topol. Appl., 119, pp. 41-51
  • Minian, E.G., Loop and suspension functors for small categories and stable homotopy groups (2003) Appl. Categor. Struct., 11, pp. 207-218
  • Minian, E.G., Numerably contractible categories (2006) K-theory, 36 (3-4), pp. 209-222
  • Quillen, D.G., Higher algebraic K-theory I (1973) Lect. Notes Math., 341, pp. 85-147
  • Segal, G., Classifying spaces and spectral sequences (1968) Publ. Math. Inst. des Hautes Etudes Scient., 34, pp. 105-112. , Paris
  • Segal, G., Categories and cohomology theories (1974) Topology, 13, pp. 293-312
  • Thomason, R.W., Cat as a closed model category (1980) Cahiers Topo, et Géom. Diff., 21 (3), pp. 305-324

Citas:

---------- APA ----------
(2006) . Spectra of small categories and infinite loop space machines. K-Theory, 37(3), 249-261.
http://dx.doi.org/10.1007/s10977-006-0017-0
---------- CHICAGO ----------
Minian, E.G. "Spectra of small categories and infinite loop space machines" . K-Theory 37, no. 3 (2006) : 249-261.
http://dx.doi.org/10.1007/s10977-006-0017-0
---------- MLA ----------
Minian, E.G. "Spectra of small categories and infinite loop space machines" . K-Theory, vol. 37, no. 3, 2006, pp. 249-261.
http://dx.doi.org/10.1007/s10977-006-0017-0
---------- VANCOUVER ----------
Minian, E.G. Spectra of small categories and infinite loop space machines. K-Theory. 2006;37(3):249-261.
http://dx.doi.org/10.1007/s10977-006-0017-0