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Book: CATEGORIES AND GROUPOIDS

CATEGORIES AND GROUPOIDS

Authors: P. J. HIGGINS

Uploaded by: bci1

Comments:
Reprints in Theory and Applications of Categories, No. 7, 1971, pp. 1--195.
Abstract:
Basic categories, groupoids and group concepts. Fundamental groupoids of topological spaces. Group and groupoid homology. Calculation of fundamental groups. Additional References [28] M. Barr and C. Wells,Toposes, triples and theories, Grundl. der Math. Wissenschaft 278 (Springer-Verlag, New York, 1984). [29] J. Benabou, Structures algebriques dans les categories, Cahiers Topologie Geom. Differentielle 10 (1968), 1--126. [30] G. Birkhoff and J. D. Lipson, Heterogeneous algebras, J. Combinatorial Theory 8 (1970), 115--133. [31] F. Borceux and G. Janelidze, Galois theories, Studies in Advanced Mathematics 72 (Cambridge University Press, 2001). [32] R. Brown, From groups to groupoids: a brief survey, Bull.London Math. Soc. 19 (1987), 113--134. [33] R. Brown and P.J.Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981), 11-14. [34] R. Brown and R. Sivera, Nonabelian algebraic topology, (in preparation). [35] R. Brown and C. B. Spencer, Double groupoids and crossed modules, Cahiers Topologie GÃeom. Differentielle 17 (1976), 343--362. [36] R Brown and A.Razak Salleh, A van Kampen theorem for unions of nonconnected spaces, Archiv. Math. 42 (1984) 85--88. [37] H. Cartan and S. Eilenberg, Homological Algebra (Princeton University Press, 1956). [38] R. B. Coates, Semantics of generalised algebraic structures (Ph. D. thesis, University of London, 1974). [39] P. M. Cohn, Universal Algebra (Harper and Row, New York, 1965). [40] A. Connes, Non--commutative geometry (Academic Press, 1994). [41] D. Corfield, Towards a philosophy of real mathematics (Cambridge University Press, 2003). [42] P. Freyd, Aspects of topoi, Bull. Australian Math. Soc. 7 (1972), 1--76. [43] P. Gabriel and F. Ulmer, Lokal prasentierbare Kategorien, Lecture Notes Transmitted to TAC by R. Brown, P.T. Johnstone, R.Street. Reprint published on 2005-01-02. 2000 Mathematics Subject Classification: 20L05, 18-01, 20E07, 20J05, 18B40, 18G30, 55Q05. Originally published by Van Nostrand Reinhold, 1971 Received by the editors 2004-08-15.
Rights:
http://www.tac.mta.ca/tac/reprints/articles/7/tr7.pdf
Links:
Physics Classification00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )
Pending Errata and Addenda
None.
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