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Simplicial sets from categories. (English) Zbl 0408.55019


MSC:

55U35 Abstract and axiomatic homotopy theory in algebraic topology
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
55U10 Simplicial sets and complexes in algebraic topology
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References:

[1] Bousfield, A.K., Kan, D.M.: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics304. Berlin-Heidelberg-New York: Springer 1970
[2] Evrard, M.: Fibrations de petites catégories. Bull. Soc. Math. France103, 241-265 (1975) · Zbl 0345.18008
[3] Fritsch, R.: Charakterisierung semisimplizialer Mengen durch Unterteilung und Graphen. Manuscripta Math.5, 213-227 (1971) · Zbl 0225.55019
[4] Fritsch, R., Latch, D.M.: Homotopy inverses for nerve. Preprint. · Zbl 0456.55013
[5] Gabriel, P., Zisman, M.: Calculus of Fractions and Homotopy Theory. Berlin-Heidelberg-New York: Springer 1967 · Zbl 0186.56802
[6] Hoff, G.: L’homotopie des categories. Cahiers Topologie Géom. Différentielle (to appear)
[7] Kan, D.M.: On c.s.s. complexes. Amer. J. Math.79, 449-476 (1957) · Zbl 0078.36901
[8] Kan, D.M.: Functors involving c.s.s. complexes. Trans. Amer. Math. Soc.87, 330-346 (1958) · Zbl 0090.39001
[9] Kan, D.M.: A combinatorial definition of homotopy groups. Ann. of Math. (2), 67, 282-312 (1958) · Zbl 0091.36901
[10] Latch, D.M.: The uniqueness of homology for the category of small categories. J. Pure Appl. Algebra9, 221-237 (1977) · Zbl 0363.18008
[11] Lee, M.J.: Homotopy for functors. Proc. Amer. Math. Soc.36, 571-577 (1972);42, 648-650 (1974) · Zbl 0256.55012
[12] MacLane, S.: Categories for the Working Mathematician. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0705.18001
[13] May, J.P.: Simplicial Objects in Algebraic Topology. Princeton, NJ: Van Nostrand 1967 · Zbl 0165.26004
[14] Milnor, J.: The geometric realization of a semi-simplicial complex. Ann. of Math. (2), 65, 357-362 (1957) · Zbl 0078.36602
[15] Segal, G.: Classifying spaces and spectral sequences. Inst. Hautes Études Sci. Publ. Math.34, 105-112 (1968) · Zbl 0199.26404
[16] Segal, G.: Categories and cohomology theories. Topology13, 293-312 (1974) · Zbl 0284.55016
[17] Spanier, E.H.: Algebraic Topology. New York-San Francisco-London: McGraw-Hill 1966 · Zbl 0145.43303
[18] Steenrod, N.E.: A convenient category of topological spaces. Michigan Math. J.14, 133-152 (1967) · Zbl 0145.43002
[19] Thomason, R.W.: Homotopy colimits in Cat, with applications to algebraicK-theory and loop space theory. Dissertation, Princeton University 1977
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