Pullback crossed modules in the category of racks

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

In this paper, we define the pullback crossed modules in the category of racks that are mainly based on a pullback diagram of rack morphisms with extra crossed module data on some of its arrows. Furthermore, we prove that the conjugation functor, which is defined between the category of crossed modules of groups and of racks, preserves the pullback crossed modules.

Keywords:

rack crossed module, limit,

PDF

___

E. Brieskorn, Automorphic sets and braids and singularities, Braids, AMS-IMS-SIAM Jt. Summer Res. Conf., Santa Cruz/Calif. 1986, Contemp. Math. 78, 45–115, 1988.
R. Brown and P. J. Higgins, On the connection between the second relative homotopy groups of some related spaces, Proc. Lond. Math. Soc. 36 (3), 192–212, 1978.
R. Brown and C. D. Wensley, On finite induced crossed modules and the homotopy 2-type of mapping cones, Theory Appl. Categ. 1, 57–71, 1995.
J. Conway and G. Wraith, Unpublished correspondence, 1959.
A. S. Crans and F. Wagemann, Crossed modules of racks, Homology Homotopy Appl. 16 (2), 85–106, 2014.
J. Faria Martins and R. Picken, Link invariants from finite categorical groups, Homology Homotopy Appl. 17 (2), 205–233, 2015.
R. Fenn and C. Rourke, Racks and links in codimension two, J. Knot Theory Ramifications, 1 (4), 343–406, 1992.
L. Kauffman, Knots and Physics, K & E series on knots and everything, World Scientific, 2001.
S. Nelson, What is...a quandle?, Notices of AMS, 63, 378–380, 2016.
D. Stanovský, Left distributive left quasigroup, Ph.D. thesis, Charles University, Prague, 2004.
J. H. C. Whitehead, On adding relations to homotopy groups, Ann. Math. 42 (2), 409–428, 1941.