BibTex RIS Kaynak Göster

On pullback and induced crossed modules of R-algebroids

Yıl 2017, Cilt: 66 Sayı: 2, 225 - 242, 01.08.2017
https://doi.org/10.1501/Commua1_0000000814

Öz

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

Kaynakça

  • 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 : osman.avcioglu@usak.edu.tr 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 : iakca@ogu.edu.tr
Yıl 2017, Cilt: 66 Sayı: 2, 225 - 242, 01.08.2017
https://doi.org/10.1501/Commua1_0000000814

Öz

Kaynakça

  • 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 : osman.avcioglu@usak.edu.tr 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 : iakca@ogu.edu.tr
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Osman Avcıoğlu Bu kişi benim

İbrahim İlker Akça Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 2

Kaynak Göster

APA Avcıoğlu, O., & Akça, İ. İ. (2017). On pullback and induced crossed modules of R-algebroids. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 225-242. https://doi.org/10.1501/Commua1_0000000814
AMA Avcıoğlu O, Akça İİ. On pullback and induced crossed modules of R-algebroids. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2017;66(2):225-242. doi:10.1501/Commua1_0000000814
Chicago Avcıoğlu, Osman, ve İbrahim İlker Akça. “On Pullback and Induced Crossed Modules of R-Algebroids”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 2 (Ağustos 2017): 225-42. https://doi.org/10.1501/Commua1_0000000814.
EndNote Avcıoğlu O, Akça İİ (01 Ağustos 2017) On pullback and induced crossed modules of R-algebroids. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 225–242.
IEEE O. Avcıoğlu ve İ. İ. Akça, “On pullback and induced crossed modules of R-algebroids”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 2, ss. 225–242, 2017, doi: 10.1501/Commua1_0000000814.
ISNAD Avcıoğlu, Osman - Akça, İbrahim İlker. “On Pullback and Induced Crossed Modules of R-Algebroids”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (Ağustos 2017), 225-242. https://doi.org/10.1501/Commua1_0000000814.
JAMA Avcıoğlu O, Akça İİ. On pullback and induced crossed modules of R-algebroids. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:225–242.
MLA Avcıoğlu, Osman ve İbrahim İlker Akça. “On Pullback and Induced Crossed Modules of R-Algebroids”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 2, 2017, ss. 225-42, doi:10.1501/Commua1_0000000814.
Vancouver Avcıoğlu O, Akça İİ. On pullback and induced crossed modules of R-algebroids. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):225-42.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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