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RELATION BETWEEN ANN-CATEGORIES AND RING CATEGORIES

Nguyen Tien Quang|Nguyen Thu Thuy|Che Thi Kim Phung
대한수학회 (The Korean Mathematical Society)|2010.10|대한수학회논문집 (Communications of the KMS)|제25권 제4호|pp. 523-535

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참고문헌

키워드

Ann-categoryring categorydistributivity constraint
주제분류수학

초록

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 x0 = y0, can be deduced from the axiomatics of an Ann-category.

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 x0 = y0, can be deduced from the axiomatics of an Ann-category.

참고문헌 (11)

  1. A. Fr¨ohlich, "Graded monoidal categories", Compos. Math., 28, pp.229~285 (1974)
  2. M. M. Kapranov, "2-categories and Zamolodchikov tetrahedra equations, Algebraic groups and their generalizations: quantum and infinite-dimensional methods", Proc. Sympos. Pure Math., 통권 : 56, pp.177~259 (1994)
  3. M. L. Laplaza, "Coherence for distributivity, Coherence in categories", Lecture Notes in Math., 통권 : 281, pp.29~65 (1972), Springer
  4. M. L. Laplaza, "Coherence for categories with group structure: an alternative approach", J. Algebra, 84(2), pp.305~323 (1983)
  5. S. Mac Lane, "Homologie des anneaux et des modules, 1957 Colloque de topologie algebrique", pp.55~80 (1956), Masson & Cie
  6. N. T. Quang, "Introduction to Ann-categories", Ta.p ch´ı To´an ho.c, 15(4), pp.14~24 (1987)
  7. N. T. Quang, "Ann-categories and the Mac Lane-Shukla cohomology of rings", Abelian groups and modules, (11), pp.166~183 (1994), Tomsk. Gos. Univ.
  8. "2009", 20
  9. N. Saavedra Rivano, "Cat´egories Tannakiennes", Lecture Notes in Math., 통권 : 265 (1972), Spriger-Verlag
  10. U. Shukla, "Cohomologie des algebras associatives", Ann. Sci. ´Ecole Norm. Sup., 7, pp.163~209 (1961)
  11. H. X. Sinh, "Gr-cat´egories, Universit´e Paris VII" (1975), Th`ese de doctorat

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