JOURNAL BROWSE
Search
Advanced SearchSearch Tips
RELATION BETWEEN ANN-CATEGORIES AND RING CATEGORIES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
RELATION BETWEEN ANN-CATEGORIES AND RING CATEGORIES
Phung, Che Thi Kim; Quang, Nguyen Tien; Thuy, Nguyen Thu;
  PDF(new window)
 Abstract
There are different categorifications of the notion of a ring such as Ann-category due to N. T. Quang, ring category due to M. M. Kapranov and V. A. Voevodsky. The main result of this paper is to prove that every axiom in the definition of a ring category, but the axiom , can be deduced from the axiomatics of an Ann-category.
 Keywords
Ann-category;ring category;distributivity constraint;
 Language
English
 Cited by
1.
DUALS OF ANN-CATEGORIES,;;

대한수학회논문집, 2012. vol.27. 1, pp.23-36 crossref(new window)
1.
DUALS OF ANN-CATEGORIES, Communications of the Korean Mathematical Society, 2012, 27, 1, 23  crossref(new windwow)
 References
1.
A. Frohlich and C. T. C. Wall, Graded monoidal categories, Compos. Math. 28 (1974), 229–285.

2.
M. M. Kapranov and V. A. Voevodsky, 2-categories and Zamolodchikov tetrahedra equations, Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), 177–259, Proc. Sympos. Pure Math., 56, Part 2, Amer. Math. Soc., Providence, RI, 1994.

3.
M. L. Laplaza, Coherence for distributivity, Coherence in categories, pp. 29–65. Lecture Notes in Math., Vol. 281, Springer, Berlin, 1972.

4.
M. L. Laplaza, Coherence for categories with group structure: an alternative approach, J. Algebra 84 (1983), no. 2, 305–323.

5.
S. Mac Lane, Homologie des anneaux et des modules, 1957 Colloque de topologie algebrique, Louvain, 1956 pp. 55–80 Georges Thone, Liege; Masson & Cie, Paris.

6.
N. T. Quang, Introduction to Ann-categories, Tap chi Toan hoc 15 (1987), no. 4, 14–24.

7.
N. T. Quang, Ann-categories and the Mac Lane-Shukla cohomology of rings, Abelian groups and modules, No. 11, 12 (Russian), 166–183, 257, Tomsk. Gos. Univ., Tomsk, 1994.

8.
N. T. Quang, Structure of Ann-categories, arXiv. 0805. 1505 v4 [math. CT] 20 Apr 2009.

9.
N. Saavedra Rivano. Categories Tannakiennes, Lecture Notes in Math. vol. 265, Spriger-Verlag, Berlin and New York, 1972.

10.
U. Shukla, Cohomologie des algebras associatives, Ann. Sci. Ecole Norm. Sup. 7 (1961), 163–209.

11.
H. X. Sinh, Gr-categories, Universite Paris VII, These de doctorat, 1975.