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Weak homomorphisms of coalgebras beyond Set

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Języki publikacji
EN
Abstrakty
EN
We study the notion of weak homomorphisms between coalgebras of different types generalizing thereby that of homomorphisms for similarly typed coalgebras. This helps extend some results known so far in the theory of Universal coalgebra over Set. We find conditions under which coalgebras of a set of types and weak homomorphisms between them form a category. Moreover, we establish an Isomorphism Theorem that extends the so-called First Isomorphism Theorem, showing thereby that this category admits a canonical factorization structure for morphisms.
Wydawca
Rocznik
Strony
555--580
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Department of Mathematics, Laboratory of Algebra Faculty of Science, University of Yaounde 1 P.O. Box 812 Yaounde, Republic of Cameroon
Bibliografia
  • [1] J. Adámek, Introduction to coalgebra, Theory Appl. Categ. 14(8) (2005), 157–199.
  • [2] J. Adámek, H. Herrlich, G. E. Strecker, Abstract and Concrete Categories, John Willey and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore, 1990.
  • [3] J. Adámek, H.-E. Porst, On Varieties and Covarieties in a Category, Preprint under consideration for publication in Math. Struct. in Comp. Science, Received February (2002).
  • [4] M. Barr, Terminal coalgebras in well-founded set theory, Theoret. Comput. Sci. 114(2) (1993), 299–315.
  • [5] M. Barr, C. Wells, Toposes, Triples and Theories, Springer, New York, Berlin, Heidelberg, Tokyo, 1985.
  • [6] A. Carboni, P. T. Johnstone, Connected limits, familial representability and Artin gluing, Math. Structures Comput. Sci. 5 (1995), 441–459.
  • [7] K. Denecke, W. Supaporn, Weak homomorphisms for (F1, F2)-systems, Slides presented at the Institute of Mathematics, University of Postdam, Germany, September 10, 2009.
  • [8] H. P. Gumm, Elements of the general theory of coalgebras, LUATCS’99, Rand Africaans University, Johannesburg, South Africa, 1999.
  • [9] H. P. Gumm, T. Schröder, Products of coalgebras, Algebra Universalis 46 (2001), 163–185.
  • [10] H. P. Gumm, T. Schröder, Types and coalgebraic structure, Algebra Universalis 53 (2005), 229–252.
  • [11] J. Hughes, A study of categories of algebras and coalgebras, PhD shesis, Carnegie Mellon University, Pittsburg PA 1213, May, 2001.
  • [12] P. T. Johnstone, A. J. Power, H. Watanabe, T. Tsujishita, J. Worrell, On the structure of categories of coalgebras, Theoret. Comput. Sci. 260 (2001), 87–117.
  • [13] J. J. M. M. Rutten, Universal coalgebra: a theory of systems, Tech. report, CS-R962, Centrum voor Wiskunde en 1996.
  • [14] J. J. M. M. Rutten, Universal coalgebra: a theory of systems, Theoret. Comput. Sci. 249 (2000), 3–80.
  • [15] K. Saengsura, (F1, F2)-systems, Thesis, Universität Postdam, January 2009.
  • [16] F. M. Schneider, Weak homomorphisms between functorial algebras, Demonstratio Math. 44 (2011), 801–818.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-23d42973-d61d-4162-81ab-f3d21c127d5e
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