Article in volume
Authors:
Title:
Distributive categories of coalgebras
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 363-373
Received: 2021-08-14 , Revised: 2022-06-29 , Accepted: 2022-06-29 , Available online: 2023-01-13 , https://doi.org/10.7151/dmgaa.1426
Abstract:
We prove that the category of coalgebras for an endo-functor $F$ is distributive
or extensive, provided that $F$ preserves pullbacks along monomorphisms and the
underlying category is distributive or extensive.
Keywords:
coalgebra, coproduct, distributive category, pullback
References:
- J. Adámek, Introduction to coalgebra, Theory and Application of Categories, 14 (2005) 157–199.
- J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories (Wiley-Interscience, 1990).
- A. Carboni, S. Lack and R.F. C Walters, Introduction to extensive and distributive categories, J. Pure Appl. Alg. 84 (2) (1993) 145–158.
https://doi.org/10.1016/0022-4049(93)90035-R - J.R.B. Cockett, Introduction to distributive categories, Math. Structure Comput. Sci. 3 (3) (1993) 277–307.
https://doi.org/10.1017/S0960129500000232 - M. Barr, Terminal coalgebras in well-founded set theory, Theoret. Comput. Sci. 114 (2) (1993) 299–315.
https://doi.org/10.1016/0304-3975(93)90076-6 - H.P. Gumm and T. Schröder, Coalgebraic structure from weak limit preserving functors, Elect. Notes Theoret. Comput. Sci. 33 (2000) 113–133.
https://doi.org/10.1016/S1571-0661(05)80346-9 - H.P. Gumm, J. Hughes and T. Schröder, Distributivity of classes of coalgebras, Theoret. Comput. Sci. 308 (2003) 131–143.
https://doi.org/10.1016/S0304-3975(02)00582-0 - H.P. Gumm and T. Schröder, Products of coalgebras, Algebra Univ. 46 (2001) 163–185.
https://doi.org/10.1007/PL00000334 - P. Johnstone, J. Power, T. Tsujishita, H. Watanabe and J. Worrell, On the structure of categories of coalgebras, Theoret. Comput. Sci. 260 (2001) 87–117.
https://doi.org/10.1016/S0304-3975(00)00124-9 - S. Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5 (Springer-Verlag, 1971).
https://doi.org/10.1007/978-1-4612-9839-7 - J.J.M.M. Rutten, Universal coalgebra: a theory of systems, Theoret. Comput. Sci. 249 (2000) 3–80.
https://doi.org/10.1016/S0304-3975(00)00056-6 - H. Schubert, Categories (Springer-Verlag, Berlin, Heidelberg and New York, 1972).
Close