A Homotopy 2-Groupoid of a Hausdorff Space: Dedicated to Bernhard Banaschewski on his 70th birthday

Applied Categorical Structures

Volumn 8, Issue 1-2, 2000, Pages 209-234

  Hardie, K A ^a   Kamps, K H ^b   Kieboom, R W ^c  

^a UNIVERSITY OF CAPE TOWN   (South Africa)

^b UNIVERSITY OF HAGEN   (Germany)

^c VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

2 groupoid; 2 track; Folding map; Fundamental groupoid; Gray tensor product; Higher homotopy structures; Homotopy; Interchange 2 track; Pasting; Piecewise linear map; Track; Tree

Indexed keywords

EID: 0000469918     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008758412196     Document Type: Article

References (39)

1. Al-Agl, F. A.: Aspects of multiple categories, Ph.D. Thesis, University of Wales, Bangor, 1989.
2. Barratt, M. G.: Track groups I, Proc. London Math. Soc. (3) 5 (1955), 71-106.
3. Baues, H. J.: Combinatorial Homotopy and 4-Dimensional Complexes, W. de Gruyter, Berlin, New York, 1981.
4. Bénabou, J.: Introduction to bicategories, in Reports of the Midwest Category Seminar, Lecture Notes in Math. 47, Springer-Verlag, Berlin, 1967, pp. 1-77.
5. Brown, R.: Groupoids and van Kampen's theorem, Proc. London Math. Soc. (3) 17 (1967), 385-401.
6. Brown, R.: Elements of Modern Topology, McGraw-Hill, Maidenhead, 1968.
7. Brown, R.: Fibrations of groupoids, J. Algebra 15 (1970), 103-132.
8. Brown, R.: Higher dimensional group theory, in Proceedings of the Conference on Topology in Low Dimension, Bangor 1979, London Math. Soc. Lecture Notes Series 48, Cambridge University Press, 1982, pp. 215-238.
9. Brown, R.: From groups to groupoids: A brief survey, Bull. London Math. Soc. 19 (1987), 113-134.
10. Brown, R.: Topology: A Geometric Account of General Topology, Homotopy Types and the Fundamental Groupoid, Ellis Horwood, Chichester, 1988.
11. Brown, R.: Homotopy theory, and change of base for groupoids and multiple groupoids, Appl. Cat. Structures 4 (1996), 175-193.
12. Brown, R.: Groupoids and crossed objects in algebraic topology, Lectures Given at the Summer School on the Foundations of Algebraic Topology, Grenoble, 1997.
13. Brown, R. and Higgins, P. J.: On the connection between the second relative homotopy groups of some related spaces, Proc. Lond. Math. Soc. (3) 36 (1978), 193-212.
14. Brown, R. and Higgins, P. J.: On the algebra of cubes, J. Pure Appl. Algebra 21 (1981), 233-260.
15. Brown, R. and Spencer, C. B.: Double groupoids and crossed modules, Cahiers Topologie Géom. Différentielle Catégoriques 17 (1976), 343-362.
16. Gabriel, P. and Zisman, M.: Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 35, Springer-Verlag, 1967.
17. Glaser, L. C.: Geometrical Combinatorial Topology, Vol. 1, Van Nostrand Reinhold Math. Stud. 27, Van Nostrand Reinhold Company, New York, 1970.
18. Grandis, M.: Categorically algebraic foundations for homotopical algebra, Appl. Cat. Structures 5 (1997), 363-413.
19. Gray, J. W.: Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Math. 391, Springer-Verlag, New York, 1974.
20. Gray, J. W.: Coherence for the tensor product of 2-categories, and braid groups, in Algebra, Topology, and Category Theory (a collection of papers in honour of Samuel Eilenberg), Academic Press, New York, 1976, pp. 63-76.
21. Hardie, K. A., Kamps, K. H. and Kieboom, R. W.: A homotopy bigroupoid of a topological space, Appl. Cat. Structures (to appear).
22. Higgins, P. J.: Notes on Categories and Groupoids, Van Nostrand Math. Stud. 32, Van Nostrand Reinhold Company, London, 1971.
23. Hilton, P. J.: An Introduction to Homotopy Theory, Cambridge Tract in Math, and Math. Phys. 43, Cambridge University Press, 1966.
24. Kelly, G. M. and Street, R.: Review of the elements of 2-categories, in Category Seminar Sydney 1972/73, Lecture Notes in Math. 420, Springer-Verlag, Berlin, 1974, pp. 75-103.
25. Loday, J.-L.: Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179-202.
26. Mac Lane, S.: Categories for the Working Mathematician, Springer-Verlag, Berlin, 1971.
27. Mather, M.: Pull-backs in homotopy theory, Canad. J. Math. 28 (1976), 225-263.
28. Moerdijk, I. and Svensson, J.-A.: Algebraic classification of equivariant homotopy 2-types, I, J. Pure Appl. Algebra 89 (1993), 187-216.
29. Porter, T.: Crossed modules in Cat and a Brown-Spencer theorem for 2-categories, Cahiers Topologie Géom. Différentielle Catégoriques 26 (1985), 381-388.
30. Rourke, C. P. and Sanderson, B. J.: Introduction to Piecewise-Linear Topology, Springer-Verlag, Berlin, 1982.
31. Rutter, J. W.: A homotopy classification of maps into an induced fibre space, Topology 6 (1967), 379-403.
32. Spanier, E. H.: Algebraic Topology, McGraw-Hill, 1966.
33. Spencer, C. B.: An abstract setting for homotopy pushouts and pullbacks, Cahiers Topologie Géom. Différentielle Catégoriques 18 (1977), 409-430.
34. Spencer, C. B. and Wong, Y. L.: Pullback and pushout squares in a special double category with connection, Cahiers Topologie Géom. Différentielle Catégoriques 24 (1983), 161-192.
35. Street, R.: Categorical structures, in M. Hazewinkel (ed.), Handbook of Algebra, Vol. 1, Elsevier, Amsterdam, 1996, pp. 529-577.
36. Teleman, C.: Généralisation du groupe fondamental, Ann. Scient. Éc. Norm. Sup. (3) 77 (1960), 195-234.
37. Whitehead, J.H.C.: On adding relations to homotopy groups, Ann. Math. 42 (1941), 409-428.
38. Whitehead, J.H.C.: Note on a previous paper entitled 'On adding relations to homotopy groups', Ann. Math. 47 (1946), 806-810.
39. Whitehead, J.H.C.: Combinatorial homotopy II, Bull. Amer. Math. Soc. 55 (1949), 453-496.