A Birkhoff-like axiomatizability result for hidden algebra and coalgebra (1998) [1 citations — 0 self]
by Grigore Rosu
Proc. of CMCS’98
http://www.cse.ucsd.edu/users/grosu/pubs/../ps/axhentcs.ps
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Abstract:
A characterization result for behaviorally definable classes of hidden algebras shows that a class of hidden algebras is behaviorally definable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a final object and an inclusion system; this is general enough to include all coalgebra categories of interest. As a technical issue, the notions of equation and satisfaction are axiomatized in order to include the different approaches in the literature. 1
Citations
| 126 | On the structure of abstract algebras – Birkhoff - 1935 |
| 44 | Logical support for modularization – Diaconescu, Goguen, et al. - 1993 |
| 27 | Burstall and Răzvan Diaconescu. Hiding and behaviour: an institutional approach – Rod - 1994 |
| 20 | Emil Căzănescu and Grigore Ros¸u. Weak inclusion systems – Virgil - 1997 |
| 19 | Coalgebra semantics for hidden algebra: parameterized objects and inheritance – Cirstea - 1998 |
| 17 | A complete calculus for equational deduction in coalgebraic specification – Corradini - 1997 |
| 7 | A semantical study of the object paradigm – Cirstea - 1996 |
