On tensor products in concrete categories

• Autorzy: Pop I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the notion of tensor product in a concrete category, in the sense of [5]. For such a tensor product, which we refer as a concrete tensor product we study some important properties: commutativity, associativity, epifunctoriality and zero object. We also consider examples and some special properties of tensor products and of concrete categories with tensor products for: arbitrary topological spaces, compact spaces, left modules, right H-comodules and left H-modules, for H a Hopf algebra.

Słowa kluczowe

EN

tensors

PL

tensory

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2000
• Tom: Vol. 33, nr 4
• Strony: 707--718
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pop I.

• Faculty of Mathematics "Al. I. Cuza University" 6600 IASI, Romania

Bibliografia

• [1] J. Činčura, Tensor products in the category of topological spaces, Comment. Math. Univ. Carolinae, vol. 20, No.3 (1979), 431-446.
• [2] J. Činčura, Tensor products in categories of topological spaces, J. Appl. Categ. Struct. 5, No.2 (1997), 111-122.
• [3] B. A. Davey, G. Davis, Tensor products and entropic varieties, Algebra Universalis 21(1985), 68-88.
• [4] S. Eilenberg, and G. M. Kelly, Closed categories, Proc. of the Conf. on Categorial Algebra, La Jolla 1965, Springer Verlag, New York 1966, 421-562.
• [5] D. Jagiello, Tensor products in concrete categories, Demonstratio Math. 32, No.2 (1999), 273-280.
• [6] G. M. Kelly, Tensor Products in Categories, J. Algebra 2(1965), 15-37.
• [7] S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS No.82 (1993), American Mathematical Socrety, Providence, R.I.
• [8] G. Radu, Algebra Categoriilor §i Functorilor, Editura Junimea, Ia§i, 1988. [Pio2] K. Pióro, A few notes on subalgebra lattices, part II- to appear in Demonstratio Math. 34(2001).