(Co)Limit calculations in the category of 2-crossed $R$-modules
Yıl: 2022 Cilt: 46 Sayı: 7 Sayfa Aralığı: 2902 - 2915 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3308 İndeks Tarihi: 12-12-2022
(Co)Limit calculations in the category of 2-crossed $R$-modules
Öz: Abstract: In this work, we obtain how to construct finite limits and colimits for 2-crossed $R$-modules over groups denoted with $X_2Mod/R$ . We give direct construction of the pullback object to show that this category has finite products over the terminal object. We also show finite coproducts and (co)completeness.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Arslan UE, Akça II, Irmak GO, Avcıoglu O. Fibrations of 2-crossed modules. Mathematical Methods in the Applied Sciences 2019; 42 (16): 5293-5304.
- [2] Arvasi Z. Crossed squares and 2-crossed modules of commutative algebras. Theory and Applications of Categories 1997; 3 (7): 160-181.
- [3] Arvasi Z, Porter T. Higher dimensional Peiffer elements in simplicial commutative algebras. Theory and Applications of Categories 1997; 3 (1): 1-23.
- [4] Arvasi Z, Ulualan E. On algebraic models for homotopy 3-types. Journal of Homotopy and Related Structures 2006; 1 (1): 1-27.
- [5] Baues HJ. Combinatorial homotopy and 4-dimensional complexes. Berlin, New York: Walter de Gruyter, 1991.
- [6] Brown R, Gilbert ND. Algebraic models of 3-types and automorphism structures for crossed modules. Proceedings of the London Mathematical Society(3) 1989; 59 (1): 51-73.
- [7] Brown R, Higgins PJ, Sivera R. Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical higher homotopy groupoids. Zurich, Switzerland: European Mathematical Society, 2011.
- [8] Brown R, Sivera R. Algebraic colimit calculations in homotopy theory using fibred and cofibred categories. Theory and Applications of Categories 2009; 22 (8): 222-251.
- [9] Carrasco P, Porter T. Coproduct of 2-crossed modules applications to a definition of a tensor product for 2-crossed complexes. Collectanea Mathematica 2016; 67 (3): 485-517.
- [10] Casas JM, Ladra M. Colimits in the crossed modules category in Lie algebras. Georgian Mathematical Journal 2000; 7 (3): 461-474.
- [11] Conduché D. Modules croisés généralisés de longueur 2. Journal of Pure and Applied Algebra 1984; 34 (2-3): 155-178.
- [12] Conduché D. Simplicial crossed modules and mapping cones. Georgian Mathematical Journal 2003; 10 (4): 623–636.
- [13] Ellis GJ. Higher dimensional crossed module of algebras. Journal of Pure and Applied Algebra 2003; 52 (3): 277-282.
- [14] Ellis GJ. Crossed squares and combinatorial homotopy. Mathematische Zeitschrift 1993; 214 (1): 93-110.
- [15] Ellis GJ, Mikhailov R. A colimit classifying spaces. Advances in Mathematics 2010; 223 (6): 2097-2113.
- [16] Guin-Waléry D, Loday J-L. Obstructioná l’excision en K-théorie algébrique, in: Algebraic K-Theory. In: Friedlander EM, Stein MR (editor) Algebraic K-Theory Evanston 1980. Berlin, Heidelberg, Germany: Springer, 1981, pp. 179- 216.
- [17] Grandjéan AR, Vale MJ. 2-Modulos cruzados an la cohomologia de André- Quillen. Memorias de la Real Academia de Ciencias 1986; 22: 1-28.
- [18] Mutlu A, Porter T. Freeness conditions for 2-crossed modules and complexes. Theory and Applications of Categories 1998; 4 (8): 174–194.
- [19] Shammu NM. Algebraic and categorical structures of category of crossed modules of algebras. PhD, University of Wales, Bangor, United Kingdom, 1992.
- [20] Whitehead JHC. Combinatorial homotopy II. Bulletin of the American Mathematical Society 1949; 55 (5): 453-496.
- [21] Yılmaz K. 2-Crossed modules over same base. Sakarya University Journal of Science 2017; 21 (6): 1210-1220.
| APA | soylu yılmaz e (2022). (Co)Limit calculations in the category of 2-crossed $R$-modules. , 2902 - 2915. 10.55730/1300-0098.3308 |
| Chicago | soylu yılmaz elis (Co)Limit calculations in the category of 2-crossed $R$-modules. (2022): 2902 - 2915. 10.55730/1300-0098.3308 |
| MLA | soylu yılmaz elis (Co)Limit calculations in the category of 2-crossed $R$-modules. , 2022, ss.2902 - 2915. 10.55730/1300-0098.3308 |
| AMA | soylu yılmaz e (Co)Limit calculations in the category of 2-crossed $R$-modules. . 2022; 2902 - 2915. 10.55730/1300-0098.3308 |
| Vancouver | soylu yılmaz e (Co)Limit calculations in the category of 2-crossed $R$-modules. . 2022; 2902 - 2915. 10.55730/1300-0098.3308 |
| IEEE | soylu yılmaz e "(Co)Limit calculations in the category of 2-crossed $R$-modules." , ss.2902 - 2915, 2022. 10.55730/1300-0098.3308 |
| ISNAD | soylu yılmaz, elis. "(Co)Limit calculations in the category of 2-crossed $R$-modules". (2022), 2902-2915. https://doi.org/10.55730/1300-0098.3308 |
| APA | soylu yılmaz e (2022). (Co)Limit calculations in the category of 2-crossed $R$-modules. Turkish Journal of Mathematics, 46(7), 2902 - 2915. 10.55730/1300-0098.3308 |
| Chicago | soylu yılmaz elis (Co)Limit calculations in the category of 2-crossed $R$-modules. Turkish Journal of Mathematics 46, no.7 (2022): 2902 - 2915. 10.55730/1300-0098.3308 |
| MLA | soylu yılmaz elis (Co)Limit calculations in the category of 2-crossed $R$-modules. Turkish Journal of Mathematics, vol.46, no.7, 2022, ss.2902 - 2915. 10.55730/1300-0098.3308 |
| AMA | soylu yılmaz e (Co)Limit calculations in the category of 2-crossed $R$-modules. Turkish Journal of Mathematics. 2022; 46(7): 2902 - 2915. 10.55730/1300-0098.3308 |
| Vancouver | soylu yılmaz e (Co)Limit calculations in the category of 2-crossed $R$-modules. Turkish Journal of Mathematics. 2022; 46(7): 2902 - 2915. 10.55730/1300-0098.3308 |
| IEEE | soylu yılmaz e "(Co)Limit calculations in the category of 2-crossed $R$-modules." Turkish Journal of Mathematics, 46, ss.2902 - 2915, 2022. 10.55730/1300-0098.3308 |
| ISNAD | soylu yılmaz, elis. "(Co)Limit calculations in the category of 2-crossed $R$-modules". Turkish Journal of Mathematics 46/7 (2022), 2902-2915. https://doi.org/10.55730/1300-0098.3308 |
