Abstract homotopy theory and generalized sheaf cohomology. (English) Zbl 0245.55007

Brown, Kenneth S.

Trans. Am. Math. Soc. 186 (1973), 419-458 (1974).

MSC:

55N30	Sheaf cohomology in algebraic topology
55N20	Generalized (extraordinary) homology and cohomology theories in algebraic topology
55T25	Generalized cohomology and spectral sequences in algebraic topology
55U99	Applied homological algebra and category theory in algebraic topology
55P99	Homotopy theory

References:

[1]	M. Artin, Grothendieck topologies, Harvard Seminar Notes, 1962. · Zbl 0208.48701
[2]	M. Artin, A. Grothendieck and J.-L. Verdier, Séminaire de géométrie algébrique; Cohomologie étale des schémas, Inst. Hautes Etudes Sci., Paris, 1963/64.
[3]	M. Artin and B. Mazur, Etale homotopy, Lecture Notes in Mathematics, No. 100, Springer-Verlag, Berlin-New York, 1969. · Zbl 0182.26001
[4]	A. K. Bousfield and D. M. Kan, Homotopy with respect to a ring, Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 59 – 64.
[5]	Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. · Zbl 0158.20505
[6]	Dan Burghelea and Aristide Deleanu, The homotopy category of spectra. I, Illinois J. Math. 11 (1967), 454 – 473. · Zbl 0164.23802
[7]	Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. · Zbl 0075.24305
[8]	Albrecht Dold, Halbexakte Homotopiefunktoren, Lecture Notes in Mathematics, vol. 12, Springer-Verlag, Berlin-New York, 1966 (German). · Zbl 0211.32801
[9]	Albrecht Dold and Dieter Puppe, Homologie nicht-additiver Funktoren. Anwendungen, Ann. Inst. Fourier Grenoble 11 (1961), 201 – 312 (German, with French summary). · Zbl 0098.36005
[10]	A. Douady, La suite spectrale de Adams: Structure multiplicative, Sém. H. Cartan, 11 (1958/59), Exposé 19.
[11]	P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag New York, Inc., New York, 1967. · Zbl 0186.56802
[12]	Roger Godement, Topologie algébrique et théorie des faisceaux, Actualit’es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958 (French). · Zbl 0080.16201
[13]	Robin Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. · Zbl 0212.26101
[14]	Daniel M. Kan, Semisimplicial spectra, Illinois J. Math. 7 (1963), 463 – 478. · Zbl 0115.40401
[15]	Daniel M. Kan, On the \?-cochains of a spectrum, Illinois J. Math. 7 (1963), 479 – 491. · Zbl 0115.40402
[16]	Daniel M. Kan and George W. Whitehead, The reduced join of two spectra, Topology 3 (1965), no. suppl. 2, 239 – 261. · Zbl 0142.40501
[17]	Daniel M. Kan and George W. Whitehead, Orientability and Poincaré duality in general homology theories, Topology 3 (1965), 231 – 270. · Zbl 0136.20005
[18]	Klaus Lamotke, Semisimpliziale algebraische Topologie, Die Grundlehren der mathematischen Wissenschaften, Band 147, Springer-Verlag, Berlin-New York, 1968 (German). · Zbl 0188.28301
[19]	J. Peter May, Simplicial objects in algebraic topology, Van Nostrand Mathematical Studies, No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. · Zbl 0769.55001
[20]	J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337 – 341. · Zbl 0114.39604
[21]	Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. · Zbl 0168.20903
[22]	George W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), 227 – 283. · Zbl 0124.38302