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Homotopy inverses for nerve
Authors:
Rudolf Fritsch and Dana May Latch
Journal:
Bull. Amer. Math. Soc. 1 (1979), 258-262
MSC (1970):
Primary 55D10, 18A40, 55D50; Secondary 55J10, 18G30, 55F35
MathSciNet review:
513754
Full-text PDF
References |
Similar Articles |
Additional Information
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May Latch, A fibred homotopy equivalence and homology theories for
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- 1.
- S. Eilenberg and J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. 51 (1950), 499-513. MR 35434
- 2.
- S. Eilenberg and S. Mac Lane, Acyclic models, Amer. J. Math. 75 (1953), 189-199.
- 3.
- R. Fritsch, Some remarks on S. Weingram: On the triangulation of a semi-simplicial complex, Illinois J. Math. 14 (1970), 529-535. MR 267569
- 4.
- P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Springer-Verlag, Berlin and New York, 1967. MR 210125
- 5.
- D. M. Kan, On c.s.s. complexes, Amer. J. Math. 79 (1957), 449-476. MR 90047
- 6.
- D. M. Kan, Functions involving c.s.s. complexes, Trans. Amer. Math. Soc. 87 (1958), 330-346. MR 131873
- 7.
- D. M. Kan, A combinational definition of homotopy groups, Ann. of Math. (2) 67 (1958), 282-312. MR 111032
- 8.
- D. M. Latch, The uniqueness of homology for the category of small categories, J. Pure Appl. Algebra 9 (1977), 221-237. MR 460421
- 9.
- D. M. Latch, A fibred homotopy equivalence and homology theories for the category of small categories, J. Pure Appl. Algebra (to appear). MR 537499
- 10.
- D. M. Latch, R. W. Thomason, and W. S. Wilson, Simplicial sets from categories, Math. Z. (to appear). MR 516607
- 11.
- M. J. Lee, Homotopy for functors, Proc. Amer. Math. Soc. 36 (1972), 571-577; 42 (1974), 648-650. MR 334212
- 12.
- A. T. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand, New York, 1969.
- 13.
- S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York, 1971. MR 354798
- 14.
- J. Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. (2) (1957), 357-362. MR 84138
- 15.
- D. G. Quillen, Homotopical algebra, Lecture Notes in Math., vol. 43, Springer-Verlag, New York, 1967. MR 223432
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- D. G. Quillen, Higher algebraic K-theory. I, Higher K-theories, Lecture Notes in Math., vol. 341, Springer-Verlag, New York, 1973, pp. 85-147. MR 338129
- 17.
- G. Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 105-112. MR 232393
- 18.
- R. W. Thomason, Cat as a closed model category (in preparation).
- 19.
- J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213-245. MR 30759
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1979-14579-8
PII:
S 0273-0979(1979)14579-8
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