Subcategories of topological algebras

Journal of Linear and Topological Algebra

مقاله 2، دوره 05، شماره 01، اردیبهشت 2016، صفحه 15-28   

نوع مقاله: Research Paper

نویسنده

V. L. Gompa^*

Department of Mathematics, Troy University, Dothan, AL 36304, USA

چکیده

In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective subcategories.

کلیدواژه‌ها

Monotopolocial category؛ topological category؛ topological functors؛ Universal algebra؛ topological algebra؛ reflective subcategory؛ coreflective subcategory, epireflective subcategory

مراجع

[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, John Wiley & Sons, Inc., New York, 1990.

[2] H. L. Bentley, H. Herrlich and R. G. Ori, Zero sets and complete regularity for nearness spaces, In: Categorical Topology, World Scientific, Teaneck, New Jersey (1989), 446-461.

[3] P. M. Cohn, Universal Algebra, Harper and Row, Publishers, New York, 1965.

[4] T. H. Fay, An axiomatic approach to categories of topological algebras, Quaestiones Mathematicae 2 (1977), 113-137.

[5] V. L. Gompa, Essentially algebraic functors and topological algebra, Indian Journal of Mathematics, 35, (1993), 189-195.

[6] H. Herrlich, Essentially algebraic categories, Quaest. Math. 9 (1986), 245-262.

[7] Y. H. Hong, Studies on categories of universal topological algebras, Doctoral Dissertation, McMaster University, 1974.

[8] H. Herrlich and G. E. Strecker, Category Theory, Allyn and Bacon, Boston, 1973.

[9] J. Koslowski, Dual adjunctions and the compatibility of structures, In: Categorical Topology, Heldermann Verlag, Berlin (1984), 308-322.

[10] J. D. Lawson and B. L. Madison, On congruences and cones, Math. Zeit. 120 (1971), 18-24.

[11] L. D. Nel, Universal topological algebra needs closed topological categories, Topology and its Applications 12 (1981) 321-330.

[12] L. D. Nel, Initially structured categories and cartesian closedness, Canad. J. Math. 27 (1975) 1361-1377.

[13] M. Petrich, Lectures in Semigroups, John Wiley & Sons, New York, 1977.

[14] W. Tholen, On Wyler's taut lift theorem, General Topology and its Applications 8 (1978), 197-206.

[15] O. Wyler, On the categories of general topology and topological algebras, Arc. Math. (Basel) 22 (1971), 7-17.