Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


Projective and injective symmetric categorical groups and duality

Author: Teimuraz Pirashvili
Journal: Proc. Amer. Math. Soc. 143 (2015), 1315-1323
MSC (2010): Primary 55-XX; Secondary 18-XX
Published electronically: October 16, 2014
MathSciNet review: 3293744
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the 2-category of symmetric categorical groups have enough projective and injective objects.

References [Enhancements On Off] (What's this?)

  • [1] Hans-Joachim Baues, Algebraic homotopy, Cambridge Studies in Advanced Mathematics, vol. 15, Cambridge University Press, Cambridge, 1989. MR 985099 (90i:55016)
  • [2] Hans-Joachim Baues, Homotopy type and homology, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1996. Oxford Science Publications. MR 1404516 (97f:55001)
  • [3] D. Bourn and E. M. Vitale, Extensions of symmetric cat-groups, Homology Homotopy Appl. 4 (2002), no. 1, 103-162. MR 1983014 (2004d:18004)
  • [4] M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory, J. Differential Geom. 70 (2005), no. 3, 329-452. MR 2192936 (2007b:53052)
  • [5] Mamuka Jibladze and Teimuraz Pirashvili, Cohomology with coefficients in stacks of abelian 2-groups, J. Pure Appl. Algebra 216 (2012), no. 10, 2274-2290. MR 2925821,
  • [6] Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872 (2001j:18001)
  • [7] H. X. Sinh, $ Gr$-catégories, Th $ \grave {e}$se de Doctoral d'Etat. Université Paris VII, 1975.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55-XX, 18-XX

Retrieve articles in all journals with MSC (2010): 55-XX, 18-XX

Additional Information

Teimuraz Pirashvili
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom

Received by editor(s): May 23, 2013
Received by editor(s) in revised form: June 9, 2013
Published electronically: October 16, 2014
Additional Notes: This research was partially supported by the grant “DI/27/5-103/12, D-13/2 Homological and categorical methods in topology, algebra and theory of stacks”
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society