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ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS

Year 2020, , 147 - 168, 07.01.2020
https://doi.org/10.24330/ieja.662998

Abstract

Concrete categories of functorial coalgebras are derived from given concrete categories under a certain commutativity condition satisfied by the underlying forgetful functor and endofunctors of its domain and codomain. When the base category is topological, so is that of functorial coalgebras when in addition to the commutativity condition the endofunctor of its domain preserves initial sources. We investigate the connection between fibres of objects in the topological category of coalgebras and those of the topological base category as well as some generalizations of the coalgebraic topological functor.

References

  • J. Adamek, Introduction to coalgebra, Theory Appl. Categ., 14(8) (2005), 157- 199.
  • J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1990.
  • J. Adamek and H.-E. Porst, On varieties and covarieties in a category, Coalgebraic methods in computer science (Genova, 2001), Math. Structures Comput. Sci., 13(2) (2003), 201-232.
  • P. Antoine, Etude elementaire des categories d'ensembles structures, Bull. Soc. Math. Belg., 18 (1966), 142-164.
  • G. C. L. Brummer, Topological categories, Topology Appl., 18(1) (1984), 27-41.
  • R. Garner, Topological functors as total categories, Theory Appl. Categ., 29(15) (2014), 406-422.
  • H. Herrlich, Topological functors, General Topology and Appl., 4 (1974), 125- 142.
  • H. Herrlich, Initial completions, Math. Z., 150(2) (1976), 101-110.
  • H. Herrlich and G. E. Strecker, Semi-universal maps and universal initial com- pletions, Paci c J. Math., 82(2) (1979), 407-428.
  • Y. H. Hong, Studies on Categories of Universal Topological Algebras, Ph.D. Thesis, McMaster Univ., Canada, 1974.
  • Y. H. Hong, On initially structured functors, J. Korean Math. Soc., 14(2) (1977/78), 159-165.
  • P. Johnstone, J. Power, T. Tsujishita, H. Watanabe and J. Worrell, On the structure of categories of coalgebras, Coalgebraic methods in computer science (Lisbon, 1998), Theoret. Comput. Sci., 260(1-2) (2001), 87-117.
  • V. Laan and S. Nasir, On mono- and epimorphisms in varieties of ordered algebras, Comm. Algebra, 43(7) (2015), 2802-2819.
  • P. Lundstrom, Weak topological functors, J. Gen. Lie Theory Appl., 2(3) (2008), 211-215.
  • L. D. Nel, Initially structured categories and Cartesian closedness, Canadian J. Math., 27(6) (1975), 1361-1377.
  • G. Preuss, Point separation axioms, monotopological categories and MacNeille completions, Category Theory at Work (Bremen, 1990), H. Herrlich, H.-E. Porst (eds.), Res. Exp. Math., Heldermann, Berlin, 18 (1991), 47-55.
  • F. Schwarz, Funktionenraume und Exponentiale Objekte in Punktetrennen Initialen Kategorien, Ph.D. Thesis, Univ. Bremen, 1983.
  • D. Zangurashvili, Effective codescent morphisms, amalgamations and factor- ization systems, J. Pure Appl. Algebra, 209(1) (2007), 255-267.
Year 2020, , 147 - 168, 07.01.2020
https://doi.org/10.24330/ieja.662998

Abstract

References

  • J. Adamek, Introduction to coalgebra, Theory Appl. Categ., 14(8) (2005), 157- 199.
  • J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1990.
  • J. Adamek and H.-E. Porst, On varieties and covarieties in a category, Coalgebraic methods in computer science (Genova, 2001), Math. Structures Comput. Sci., 13(2) (2003), 201-232.
  • P. Antoine, Etude elementaire des categories d'ensembles structures, Bull. Soc. Math. Belg., 18 (1966), 142-164.
  • G. C. L. Brummer, Topological categories, Topology Appl., 18(1) (1984), 27-41.
  • R. Garner, Topological functors as total categories, Theory Appl. Categ., 29(15) (2014), 406-422.
  • H. Herrlich, Topological functors, General Topology and Appl., 4 (1974), 125- 142.
  • H. Herrlich, Initial completions, Math. Z., 150(2) (1976), 101-110.
  • H. Herrlich and G. E. Strecker, Semi-universal maps and universal initial com- pletions, Paci c J. Math., 82(2) (1979), 407-428.
  • Y. H. Hong, Studies on Categories of Universal Topological Algebras, Ph.D. Thesis, McMaster Univ., Canada, 1974.
  • Y. H. Hong, On initially structured functors, J. Korean Math. Soc., 14(2) (1977/78), 159-165.
  • P. Johnstone, J. Power, T. Tsujishita, H. Watanabe and J. Worrell, On the structure of categories of coalgebras, Coalgebraic methods in computer science (Lisbon, 1998), Theoret. Comput. Sci., 260(1-2) (2001), 87-117.
  • V. Laan and S. Nasir, On mono- and epimorphisms in varieties of ordered algebras, Comm. Algebra, 43(7) (2015), 2802-2819.
  • P. Lundstrom, Weak topological functors, J. Gen. Lie Theory Appl., 2(3) (2008), 211-215.
  • L. D. Nel, Initially structured categories and Cartesian closedness, Canadian J. Math., 27(6) (1975), 1361-1377.
  • G. Preuss, Point separation axioms, monotopological categories and MacNeille completions, Category Theory at Work (Bremen, 1990), H. Herrlich, H.-E. Porst (eds.), Res. Exp. Math., Heldermann, Berlin, 18 (1991), 47-55.
  • F. Schwarz, Funktionenraume und Exponentiale Objekte in Punktetrennen Initialen Kategorien, Ph.D. Thesis, Univ. Bremen, 1983.
  • D. Zangurashvili, Effective codescent morphisms, amalgamations and factor- ization systems, J. Pure Appl. Algebra, 209(1) (2007), 255-267.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Maurice Kianpi This is me

Publication Date January 7, 2020
Published in Issue Year 2020

Cite

APA Kianpi, M. (2020). ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS. International Electronic Journal of Algebra, 27(27), 147-168. https://doi.org/10.24330/ieja.662998
AMA Kianpi M. ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS. IEJA. January 2020;27(27):147-168. doi:10.24330/ieja.662998
Chicago Kianpi, Maurice. “ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS”. International Electronic Journal of Algebra 27, no. 27 (January 2020): 147-68. https://doi.org/10.24330/ieja.662998.
EndNote Kianpi M (January 1, 2020) ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS. International Electronic Journal of Algebra 27 27 147–168.
IEEE M. Kianpi, “ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS”, IEJA, vol. 27, no. 27, pp. 147–168, 2020, doi: 10.24330/ieja.662998.
ISNAD Kianpi, Maurice. “ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS”. International Electronic Journal of Algebra 27/27 (January 2020), 147-168. https://doi.org/10.24330/ieja.662998.
JAMA Kianpi M. ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS. IEJA. 2020;27:147–168.
MLA Kianpi, Maurice. “ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS”. International Electronic Journal of Algebra, vol. 27, no. 27, 2020, pp. 147-68, doi:10.24330/ieja.662998.
Vancouver Kianpi M. ON THE TOPOLOGICITY OF CATEGORIES OF COALGEBRAS. IEJA. 2020;27(27):147-68.