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COLIMITS IN THE CATEGORY OF QUADRATIC MODULES

Year 2016, Volume: 65 Issue: 1, 53 - 70, 01.02.2016
https://doi.org/10.1501/Commua1_0000000744

Abstract

To use of colimits to put structures together is not uncommon inmathematics; coproducts particularly of structures such as groups and vectorspaces have been known for a long time. Colimits have also been used incomputer science for example to put together labeled graphs, in system theoryetc. The importance of category for theoretical computer scientists is everydayincreasing.…nite (co)limits in the category of quadratic modules of groups by carefulconstruction of (co)product ob ject and (co)equilaser of morphisms of quadraticmodules. Moreover, we give some examples of coproduct

References

  • Z. Arvasi and E. Ulualan, On algebraic models for homotopy 3-types, Journal of Homotopy and Related Structures, Vol.1, No.1, pp.1-27, (2006).
  • H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, 15, pages, (1991).
  • R. Brown and P.J. Higgins, Colimit-theorems for relative homotopy groups, Jour. Pure Appl. Algebra, Vol. 22, 11-41, (1981).
  • R.Brown and P.J.Higgins ‘On the connection between the second relative homotopy groups of some related spaces’, Proc. London Math. Soc., (3) 36 (1978) 193-212. R. complexes, tered http://www.bangor.ac.uk/ mas010/pd¢ les/rbrsbookb-e231109.pdf. topology: …l- spaces, crossed cubical higher homotopy groupoids
  • R. Brown and R. Sivera, Algebraic colimit calculations in homotopy theory using …bred and co…bred categories, Theory and Applications of Categories, 22 (2009) 222-251.
  • J.M. Casas and M. Ladra, Colimits in the crossed modules category in Lie algebras, Georgian Mathematical Journal, V7 N3, 461-474, 2000.
  • G.J. Ellis, Crossed squares and combinatorial homotopy , Math.Z. , 214, 93-110, (1993).
  • M.S.Nizar, Algebraic and categorical structures of category of crossed modules of algebras, Ph.D. Thesis, University of Wales,(1992).
  • T. Porter, Homology of Commutative Algebras and an Invariant of Simis and Vasconceles J.Algebra 99, 458-465, (1986).
  • T. Porter, Some categorical results in the theory of crossed modules in commutative algebras, J.Algebra 109 415-429, (1987).
  • J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc., 55, pp 453-496, (1949).
  • Current address : ·Istanbul Medeniyet University, Science Faculty, Mathematics Department, Turkey E-mail address : hasan.atik@medeniyet.edu.tr
Year 2016, Volume: 65 Issue: 1, 53 - 70, 01.02.2016
https://doi.org/10.1501/Commua1_0000000744

Abstract

References

  • Z. Arvasi and E. Ulualan, On algebraic models for homotopy 3-types, Journal of Homotopy and Related Structures, Vol.1, No.1, pp.1-27, (2006).
  • H.J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, 15, pages, (1991).
  • R. Brown and P.J. Higgins, Colimit-theorems for relative homotopy groups, Jour. Pure Appl. Algebra, Vol. 22, 11-41, (1981).
  • R.Brown and P.J.Higgins ‘On the connection between the second relative homotopy groups of some related spaces’, Proc. London Math. Soc., (3) 36 (1978) 193-212. R. complexes, tered http://www.bangor.ac.uk/ mas010/pd¢ les/rbrsbookb-e231109.pdf. topology: …l- spaces, crossed cubical higher homotopy groupoids
  • R. Brown and R. Sivera, Algebraic colimit calculations in homotopy theory using …bred and co…bred categories, Theory and Applications of Categories, 22 (2009) 222-251.
  • J.M. Casas and M. Ladra, Colimits in the crossed modules category in Lie algebras, Georgian Mathematical Journal, V7 N3, 461-474, 2000.
  • G.J. Ellis, Crossed squares and combinatorial homotopy , Math.Z. , 214, 93-110, (1993).
  • M.S.Nizar, Algebraic and categorical structures of category of crossed modules of algebras, Ph.D. Thesis, University of Wales,(1992).
  • T. Porter, Homology of Commutative Algebras and an Invariant of Simis and Vasconceles J.Algebra 99, 458-465, (1986).
  • T. Porter, Some categorical results in the theory of crossed modules in commutative algebras, J.Algebra 109 415-429, (1987).
  • J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc., 55, pp 453-496, (1949).
  • Current address : ·Istanbul Medeniyet University, Science Faculty, Mathematics Department, Turkey E-mail address : hasan.atik@medeniyet.edu.tr
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Hasan Atik This is me

Publication Date February 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 1

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APA Atik, H. (2016). COLIMITS IN THE CATEGORY OF QUADRATIC MODULES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 53-70. https://doi.org/10.1501/Commua1_0000000744
AMA Atik H. COLIMITS IN THE CATEGORY OF QUADRATIC MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2016;65(1):53-70. doi:10.1501/Commua1_0000000744
Chicago Atik, Hasan. “COLIMITS IN THE CATEGORY OF QUADRATIC MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 1 (February 2016): 53-70. https://doi.org/10.1501/Commua1_0000000744.
EndNote Atik H (February 1, 2016) COLIMITS IN THE CATEGORY OF QUADRATIC MODULES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 53–70.
IEEE H. Atik, “COLIMITS IN THE CATEGORY OF QUADRATIC MODULES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 53–70, 2016, doi: 10.1501/Commua1_0000000744.
ISNAD Atik, Hasan. “COLIMITS IN THE CATEGORY OF QUADRATIC MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February 2016), 53-70. https://doi.org/10.1501/Commua1_0000000744.
JAMA Atik H. COLIMITS IN THE CATEGORY OF QUADRATIC MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:53–70.
MLA Atik, Hasan. “COLIMITS IN THE CATEGORY OF QUADRATIC MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, 2016, pp. 53-70, doi:10.1501/Commua1_0000000744.
Vancouver Atik H. COLIMITS IN THE CATEGORY OF QUADRATIC MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):53-70.

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

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