On pullback and induced crossed modules of R-algebroids

Year 2017, Volume: 66 Issue: 2, 225 - 242, 01.08.2017

Osman Avcıoğlu İbrahim İlker Akça

https://doi.org/10.1501/Commua1_0000000814

Cited By: 1

Abstract

In this paper we study the pullback and induced crossed modules of R-algebroids, prove that the related induced crossed module functor isthe left adjoint of the related pullback crossed module functor and give someconsequences of the adjunction

Keywords

Algebroids, crossed modules of algebroids, adjoint functors

References

• Alp, M., Pullback crossed modules of algebroids, Iran. J. Sci. Technol. (2008), 32(A1), 1-5.
• Alp, M., Pushout crossed modules of algebroids, Iran. J. Sci. Technol. (2008), 32(A3), 175
• Amgott, S.M., Separable Categories, J. Pure. Appl. Algebra (1986), 40, 1-14.
• Arvasi, Z. and Porter, T., Simplicial and crossed resolutions of commutative algebras, J. Algebra (1996), 181, 426-448.
• Arvasi, Z., Crossed Modules of Algebras, Math. Comput. Appl. (2004), 9(2), 173-182.
• Avcıo¼glu, O. and Akça, ·I.·I., Free modules and crossed modules of R-algebroids, Submitted to Turk. J. Math. Brown, R. and Higgins, P.J., On the Connection Between the Second Relative Homotopy Groups of Some Related Spaces, Proc. London Math. Soc. (1978), 36, 193-212.
• Brown, R., Higgins, P.J. and Sivera, R., Nonabelian Algebraic Topology. EMS Tracts in Mathematics Vol.15 2011.
• Brown, R. and ·Içen ·I., Homotopies and Automorphisms of Crossed Modules of Groupoids, Applied Categorical Structures (2003), 11, 185-206.
• Brown, R. and Wensley C.D., On Finite Induced Crossed Modules, and The Homotopy 2- Type of Mapping Cones, Theory and Applications of Categories (1995), 1(3), 54-71.
• Gerstenhaber, M., On the deformation of rings and algebras: II, Ann. of Math. (1966), 84, 19.
• Lichtenbaum, S. and Schlessinger, M., The Cotangent Complex of a Morphism, Trans. Amer. Math. Soc. (1967), 128, 41-70.
• Lue, A.S.T., Non-abelian cohomology of associative algebras, Q. J. Math. (1968), 19(1), 180.
• Mitchell, B., Rings with several ob jects, Adv. in Math. (1972), 8(1), 1-161.
• Mitchell, B., Some applications of module theory to functor categories, Bull. Amer. Math. Soc. (1978), 84, 867-885.
• Mitchell, B., Separable Algebroids, Mem. Amer. Math. Soc. 57 (1985), no. 333, 96 pp.
• Mosa, G.H., Higher Dimensional Algebroids and Crossed Complexes, PhD Thesis, University of Wales, Bangor, 1986. groupoids.org.uk/mosa-thesis.html Shammu, N.M., of categorical structure of Wales, modules http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304282 PhD Thesis, University of Bangor
• Porter, T., The Crossed Manegarie: An introduction to crossed gadgetry and cohomology in algebra and topology, 9 February 2010. https://ncatlab.org/timporter/…les/menagerie10.pdf
• Porter, T., Homology of commutative algebras and an invariant of Simis and Vasconcelos. J. Algebra (1986), 99, 458-465.
• Porter, T., Some categorical results in the theory of crossed modules in commutative algebras, J. Algebra (1987), 109, 415-429.
• Whitehead, J.H.C., On adding relations to homotopy groups, Ann. of Math. 1941, 42, 409
• Whitehead, J.H.C., Note on a previous paper entitled “On adding relations to homotopy groups.”, Ann. of Math. (1946), 47, 806-810.
• Current address : Osman Avcıo¼glu: Usak University, Faculty of Arts and Sciences, Department of Mathematics, 64200 - Usak, Turkey.
• E-mail address : [e-mail] Current address : ·Ibrahim ·Ilker Akça: Eskisehir Osmangazi University, Faculty of Science and Letters, Department of Mathematics and Computer Sciences, 26480 - Eskisehir, Turkey.
• E-mail address : [e-mail]