Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 2, 86 - 95, 15.10.2020
https://doi.org/10.36753/mathenot.691956

Öz

Kaynakça

  • [1] Baez, J.C., Baratin, A., Freidel, L. and Wise, D.K.: Infinite-Dimensional Representations of 2-Groups. Mem. Am. Math. Soc. 219, (1032) (2012).
  • [2] Baez, J.C., Lauda, A.D.: Higher Dimensional Algebra V: 2-Groups. Theory Appl. Categ. 12, 423–491 (2004).
  • [3] Brown, R.: Topology and Groupoids. BookSurge LLC, North Carolina (2006).
  • [4] Brown, R, Spencer, C.B.: Double groupoids and crossed modules. Cahiers de Topologie et Géométrie Différentielle Catégoriques 17 (4), 343-362 (1976).
  • [5] Brown, R., Spencer, C.B.: G-groupoids, crossed modules and the fundamental groupoid of a topological group. Mathematical Sciences and Applications E-Notes. Indagat. Math. 79 (4), 296-302 (1976).
  • [6] Brown, R., Higgins, P. J. and Sivera, R.: Nonabelian Algebraic Topology: Filtered spaces, crossed complexes, cubical homotopy groupoids. European Mathematical Society Tracts in Mathematics 15 (2011).
  • [7] Brown, R., Mucuk, O.: Covering groups of non-connected topological groups revisited. Math. Proc. Camb. Phil. Soc. 115, 97–110 (1994).
  • [8] Ehresmann, C.: Catégories doubles et catégories structurées. C. R. Acad. Sci. Paris 256, 1198-1201 (1963).
  • [9] Ehresmann, C.: Catégories structurées. Ann. Sci. Ec. Norm. Super. 80, 349-425 (1963b).
  • [10] Huebschmann, J.: Crossed n-fold extensions of groups and cohomology. Comment. Math. Helvetici. 55: 302-314 (1980).
  • [11] Kerler, T. and Lyubashenko, V.V.: Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners. Springer-Verlag. Berlin, Heidelberg, (2001).
  • [12] Loday, J.-L.: Cohomologie et groupes de Steinberg relatifs. J. Algebra. 54 178-202 (1978).
  • [13] Maclane, S.: Categories for the Working Mathematician, Graduate Text in Mathematics. 5, Springer-Verlag. New York (1971).
  • [14] Mucuk, O., Demir S.: Normality and quotient in crossed modules over groupoids and double groupoids. Turk J Math, 42, 2336 – 2347 (2018).
  • [15] Patchkoria, A.: Crossed Semimodules and Schreier Internal Categories In The Category of Monoids. Georgian Math. J. 5(6), 575-581 (1998).
  • [16] Porter, T.: Crossed Modules in Cat and a Brown-Spencer Theorem for 2-Categories. Cah. Topol. Géom. Différ. Catég. XXVI-4 (1985).
  • [17] ¸Sahan, T., Mohammed, J.J.: Categories internal to crossed modules Sakarya University Journal of Science. 23 (4), 519-531, (2019).
  • [18] Temel, S., ¸Sahan, T. and Mucuk, O.: Crossed modules, double group-groupoids and crossed squares. Preprint arxiv:1802.03978v2 (2018).
  • [19] Temel, S.: Topological Crossed Semimodules and Schreier Internal Categories in the Category of Topological Monoids. Gazi University Journal of Science. 29 (4), 915-921 (2016).
  • [20] Temel, S.: Crossed semimodules of categories and Schreier 2-categories. Tbilisi Math. J. 11 (2), 47-57 (2018).
  • [21] Temel, S.: Normality and quotient in crossed modules over groupoids and 2-groupoids. Korean J. Math. 27 (1), 151-163 (2018).
  • [22] Whitehead, J.H.C.: Combinatorial homotopy II. Bull. Amer. Math. Soc. 55, 453-496 (1949).
  • [23] Whitehead, J.H.C.: Note on a previous paper entitled "On adding relations to homotopy group". Ann. Math. 47,806-810 (1946).

Internal Categories in Crossed Semimodules and Schreier Internal Categories

Yıl 2020, Cilt: 8 Sayı: 2, 86 - 95, 15.10.2020
https://doi.org/10.36753/mathenot.691956

Öz

In this paper, we characterize internal categories in the category of crossed semimodules and the category of Schreier internal categories within monoids. Then we prove a natural equivalence between their categories. This allows us to produce various examples of double categories.                                                                                                                                                                                                                                                                                                          .

Kaynakça

  • [1] Baez, J.C., Baratin, A., Freidel, L. and Wise, D.K.: Infinite-Dimensional Representations of 2-Groups. Mem. Am. Math. Soc. 219, (1032) (2012).
  • [2] Baez, J.C., Lauda, A.D.: Higher Dimensional Algebra V: 2-Groups. Theory Appl. Categ. 12, 423–491 (2004).
  • [3] Brown, R.: Topology and Groupoids. BookSurge LLC, North Carolina (2006).
  • [4] Brown, R, Spencer, C.B.: Double groupoids and crossed modules. Cahiers de Topologie et Géométrie Différentielle Catégoriques 17 (4), 343-362 (1976).
  • [5] Brown, R., Spencer, C.B.: G-groupoids, crossed modules and the fundamental groupoid of a topological group. Mathematical Sciences and Applications E-Notes. Indagat. Math. 79 (4), 296-302 (1976).
  • [6] Brown, R., Higgins, P. J. and Sivera, R.: Nonabelian Algebraic Topology: Filtered spaces, crossed complexes, cubical homotopy groupoids. European Mathematical Society Tracts in Mathematics 15 (2011).
  • [7] Brown, R., Mucuk, O.: Covering groups of non-connected topological groups revisited. Math. Proc. Camb. Phil. Soc. 115, 97–110 (1994).
  • [8] Ehresmann, C.: Catégories doubles et catégories structurées. C. R. Acad. Sci. Paris 256, 1198-1201 (1963).
  • [9] Ehresmann, C.: Catégories structurées. Ann. Sci. Ec. Norm. Super. 80, 349-425 (1963b).
  • [10] Huebschmann, J.: Crossed n-fold extensions of groups and cohomology. Comment. Math. Helvetici. 55: 302-314 (1980).
  • [11] Kerler, T. and Lyubashenko, V.V.: Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners. Springer-Verlag. Berlin, Heidelberg, (2001).
  • [12] Loday, J.-L.: Cohomologie et groupes de Steinberg relatifs. J. Algebra. 54 178-202 (1978).
  • [13] Maclane, S.: Categories for the Working Mathematician, Graduate Text in Mathematics. 5, Springer-Verlag. New York (1971).
  • [14] Mucuk, O., Demir S.: Normality and quotient in crossed modules over groupoids and double groupoids. Turk J Math, 42, 2336 – 2347 (2018).
  • [15] Patchkoria, A.: Crossed Semimodules and Schreier Internal Categories In The Category of Monoids. Georgian Math. J. 5(6), 575-581 (1998).
  • [16] Porter, T.: Crossed Modules in Cat and a Brown-Spencer Theorem for 2-Categories. Cah. Topol. Géom. Différ. Catég. XXVI-4 (1985).
  • [17] ¸Sahan, T., Mohammed, J.J.: Categories internal to crossed modules Sakarya University Journal of Science. 23 (4), 519-531, (2019).
  • [18] Temel, S., ¸Sahan, T. and Mucuk, O.: Crossed modules, double group-groupoids and crossed squares. Preprint arxiv:1802.03978v2 (2018).
  • [19] Temel, S.: Topological Crossed Semimodules and Schreier Internal Categories in the Category of Topological Monoids. Gazi University Journal of Science. 29 (4), 915-921 (2016).
  • [20] Temel, S.: Crossed semimodules of categories and Schreier 2-categories. Tbilisi Math. J. 11 (2), 47-57 (2018).
  • [21] Temel, S.: Normality and quotient in crossed modules over groupoids and 2-groupoids. Korean J. Math. 27 (1), 151-163 (2018).
  • [22] Whitehead, J.H.C.: Combinatorial homotopy II. Bull. Amer. Math. Soc. 55, 453-496 (1949).
  • [23] Whitehead, J.H.C.: Note on a previous paper entitled "On adding relations to homotopy group". Ann. Math. 47,806-810 (1946).
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Sedat Temel 0000-0001-6553-8758

Yayımlanma Tarihi 15 Ekim 2020
Gönderilme Tarihi 21 Şubat 2020
Kabul Tarihi 17 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

APA Temel, S. (2020). Internal Categories in Crossed Semimodules and Schreier Internal Categories. Mathematical Sciences and Applications E-Notes, 8(2), 86-95. https://doi.org/10.36753/mathenot.691956
AMA Temel S. Internal Categories in Crossed Semimodules and Schreier Internal Categories. Math. Sci. Appl. E-Notes. Ekim 2020;8(2):86-95. doi:10.36753/mathenot.691956
Chicago Temel, Sedat. “Internal Categories in Crossed Semimodules and Schreier Internal Categories”. Mathematical Sciences and Applications E-Notes 8, sy. 2 (Ekim 2020): 86-95. https://doi.org/10.36753/mathenot.691956.
EndNote Temel S (01 Ekim 2020) Internal Categories in Crossed Semimodules and Schreier Internal Categories. Mathematical Sciences and Applications E-Notes 8 2 86–95.
IEEE S. Temel, “Internal Categories in Crossed Semimodules and Schreier Internal Categories”, Math. Sci. Appl. E-Notes, c. 8, sy. 2, ss. 86–95, 2020, doi: 10.36753/mathenot.691956.
ISNAD Temel, Sedat. “Internal Categories in Crossed Semimodules and Schreier Internal Categories”. Mathematical Sciences and Applications E-Notes 8/2 (Ekim 2020), 86-95. https://doi.org/10.36753/mathenot.691956.
JAMA Temel S. Internal Categories in Crossed Semimodules and Schreier Internal Categories. Math. Sci. Appl. E-Notes. 2020;8:86–95.
MLA Temel, Sedat. “Internal Categories in Crossed Semimodules and Schreier Internal Categories”. Mathematical Sciences and Applications E-Notes, c. 8, sy. 2, 2020, ss. 86-95, doi:10.36753/mathenot.691956.
Vancouver Temel S. Internal Categories in Crossed Semimodules and Schreier Internal Categories. Math. Sci. Appl. E-Notes. 2020;8(2):86-95.

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