Isomorphism Theorems for Coalgebras

Jean-Paul Mavoungou

doi:10.2478/amsil-2018-0014

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Isomorphism Theorems for Coalgebras

Annales Mathematicae Silesianae

Volume 33 (2019): Issue 1 (September 2019)

By: Jean-Paul Mavoungou

Open Access

|Jul 2019

Abstract

Let F be an endofunctor of a category C. We prove isomorphism theorems for F -coalgebras under condition that the underlying category C is exact; that is, regular with exact sequences. Also, F is not assumed to preserve pullbacks.

References

[1] P. Aczel and N. Mendler, A final coalgebra theorem, in: D.H. Pitt et al. (Eds.), Category Theory and Computer Science, Lecture Notes in Comput. Sci., 389, Springer, Berlin, 1989, pp. 357–365.10.1007/BFb0018361
Search in Google Scholar Back to article
[2] M. Barr and C. Wells, Toposes, Triples and Theories. Corrected reprint of the 1985 original. Repr. Theory Appl. Categ. 12 (2005), 1–288.10.1007/978-1-4899-0021-0_8
Search in Google Scholar Back to article
[3] H.P. Gumm, Elements of the general theory of coalgebras, LUATCS’99, Rand Africaans University, Johannesburg, South Africa, 1999.
Search in Google Scholar Back to article
[4] P.T. Johnstone, Topos Theory, Academic Press, London-New York, 1977.
Search in Google Scholar Back to article
[5] P. Johnstone, J. Power, T. Tsujishita, H. Watanabe, and J. Worrell, On the structure of categories of coalgebras, Theoret. Comput. Sci. 260 (2001), no. 1–2, 87–117.10.1016/S0304-3975(00)00124-9
Search in Google Scholar Back to article
[6] J.J.M.M. Rutten, Universal coalgebra: a theory of systems, Theoret. Comput. Sci. 249 (2000), no. 1, 3–80.10.1016/S0304-3975(00)00056-6
Search in Google Scholar Back to article
[7] S. Staton, Relating coalgebraic notions of bisimulation, Log. Methods Comput. Sci. 7 (2011), no. 1, 1:13, 21 pp.10.2168/LMCS-7(1:13)2011
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2018-0014 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 210 - 220

Submitted on: Feb 23, 2018

Accepted on: Oct 28, 2018

Published on: Jul 18, 2019

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

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© 2019 Jean-Paul Mavoungou, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 33 (2019): Issue 1 (September 2019)