Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Homotopy inverses for nerve

Author(s): Rudolf Fritsch; 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
Retrieve article in: PDF

References | Similar articles | Additional information

References:

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
16.
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

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 55D10, 18A40, 55D50, 55J10, 18G30, 55F35

Retrieve articles in all Journals with MSC (1970): 55D10, 18A40, 55D50, 55J10, 18G30, 55F35


Additional Information:

DOI: 10.1090/S0273-0979-1979-14579-8
PII: S 0273-0979(1979)14579-8


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google