본문 바로가기
KERD
논문KCI 등재

Derived crossed modules

Tunçar Şahan
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2018.09|한국수학논문집 (Korean Journal of Mathematics)|제26권 제3호|pp. 439-458

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

crossed moduleHomotopyinternal categorygroup with operations
주제분류수학

초록

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\C$ of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in $\C$. Further, we characterize the derivations of crossed modules in a category $\C$ and obtain new crossed modules using regular derivations of old one.

Abstract

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\C$ of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in $\C$. Further, we characterize the derivations of crossed modules in a category $\C$ and obtain new crossed modules using regular derivations of old one.

참고문헌 (25)

  1. H. F. Akiz, "Coverings of internal groupoids and crossed modules in the category of groups with operations", Georgian Math. J., 20(2), pp.223~238 (2013)
  2. J. C. Baez, "The Classifying Space of a Topological 2-Group;Algebraic Topology", Abel Symposia, pp.1~31 (2009)
  3. R. Brown, "Groupoids and crossed objects in algebraic topology Homol", Homotopy Appl., 1, pp.1~78 (1999)[DOI]
  4. R. Brown, "London Mathematical Society Lecture Note Series", pp.153~202 (1982), Cambridge University Press
  5. R. Brown, "G-groupoids, crossed modules and the fundamental groupoid of a topological group", Indagat. Math., 79(4), pp.296~302 (1976)[DOI]
  6. W. H. Cockcroft, "On the homomorphisms of sequences", Math. Proc. Cambridge, 48(4), pp.521~532 (1952)[DOI]
  7. T. Datuashvili, "Cohomologically trivial internal categories in categories of groups with operations", Appl. Categor. Struct., 3(3), pp.221~237 (1995)[DOI]
  8. T. Datuashvili, "Categorical, homological and homotopical properties of algebraic objects", pp.2006
  9. J. Huebschmann, "Crossed n-folds extensions of groups and cohomology", Comment. Math. Helv., 55, pp.302~313 (1980)[DOI]
  10. J.-L. Loday, "Cohomologie et groupe de steinberg relatifs", J. Algebra, 54(1), pp.178~202 (1978)[DOI]
  11. A. S.-T. Lue, "Cohomology of groups relative to a variety", J. Algebra, 69(1), pp.155~174 (1981)[DOI]
  12. O. Mucuk, "Monodromy groupoid of an internal groupoid in topological groups with operations", Filomat, 29(10), pp.2355~2366 (2015)[DOI]
  13. O. Mucuk, "G-connectedness in topological groups with operations", Filomat, 32(3), pp.1079~1089 (2018)
  14. O. Mucuk, "Coverings and crossed modules of topological groups with operations", Turk. J. Math., 38(5), pp.833~845 (2014)[DOI]
  15. K. Norrie, "Actions and automorphisms of crossed modules", Bull. Soc. Math. Fr., 118(2), pp.129~146 (1990)[DOI]
  16. G. Orzech, "Obstruction theory in algebraic categories, I", J. Pure. Appl. Algebra, 2(4), pp.287~314 (1972)[DOI]
  17. G. Orzech, "Obstruction theory in algebraic categories, II", J. Pure. Appl. Algebra, 2(4), pp.315~340 (1972)[DOI]
  18. A. Patchkoria, "Crossed semimodules and schreier internal categories in the category of monoids", Georgian Math. J., 5(6), pp.575~581 (1998)[DOI]
  19. T. Porter, "Extensions, crossed modules and internal categories in categories of groups with operations", P. Edinburgh. Math. Soc., 30(3), pp.373~381 (1987)[DOI]
  20. T. Sahan, "Further remarks on liftings of crossed modules", Hacet. J. Math. Stat. (2018)
  21. S. Temel, "Topological crossed semimodules and schreier internal categories in the category of topological monoids", Gazi Univ. J. Sci., 29(4), pp.915~921 (2016)
  22. S. Temel, "Crossed semimodules of categories and Schreier 2-categories", Tbilisi Math. J., 11(2), pp.47~57 (2018)
  23. J. H. C. Whitehead, "Note on a previous paper entitled "on adding relations to homotopy groups"", Ann. Math., 47(4), pp.806~810 (1946)[DOI]
  24. J. H. C. Whitehead, "On operators in relative homotopy groups", Ann. Math., 49(3), pp.610~640 (1948)[DOI]
  25. J. H. C. Whitehead, "Combinatorial homotopy. II", Bull. Amer. Math. Soc., 55(5), pp.453~496 (1949)[DOI]

관련 논문AI추천

Generalized crossed modules over generalized group-groupoidsH. Fulya Akız강원경기수학회 · 한국수학논문집2024 · 제32권 제1호Crossed semimodules and cat$^{\bf 1}$-monoidsSedat Temel강원경기수학회 · 한국수학논문집2019 · 제27권 제2호Normality and quotient in crossed modules over groupoids and 2-groupoidsSedat Temel강원경기수학회 · 한국수학논문집2019 · 제27권 제1호EQUIVARIANT CROSSED MODULES AND COHOMOLOGY OF GROUPS WITH OPERATORSNguyen Tien Quang, Pham Thi Cuc대한수학회 · 대한수학회보2015 · 제52권 제4호Crossed modules and strict Gr-categoriesNguyen Thu Thuy, Nguyen Tien Quang, Pham Thi Cuc대한수학회 · 대한수학회논문집2014 · 제29권 제1호On the geometry of the crossed product of groupsAhmet Sinan Cevik, Eylem Guzel Karpuz, Firat Ates대한수학회 · 대한수학회보2021 · 제58권 제5호

이 간행물의 다른 논문 (11건)

Inequalities for quantum $f$-divergence of convex functions and matricesSilvestru Sever Dragomirpp. 349-371Fuzzy homomorphism theorems on groupsGezahagne Mulat Addispp. 373-385Shifting and modulation for the convolution product of functionals in a generalized Fresnel class김병수, 박연희pp. 387-403Growth analysis of composite entire functions from the view point of relative $(p,q)$-th orderTanmay Biswaspp. 405-424Surfaces generated via the evolution of spherical image of a space curveTaha Youssef Shaker, R. A. Hussien, M. A. Soliman, Nassar H.Abdel-Allpp. 425-437
원문 보기