Universal Dialgebra: Unifying Universal Algebra and Coalgebra
نویسنده
چکیده
The concept of dialgebra provides a platform under which universal algebra and coalgebra are unified in one theory. Other examples of dialgebras include universal multialgebras and partial algebras. In the dialgebraic setting, several relationships between common features of these various theories are clarified and, in many cases, rather similar proofs of closely related results are combined to a single proof. Moreover, as has been recently conjectured in the context of behavioral certification of evolving software requirements, this more general setting increases the potential of application of the various constituent theories by combining many of the desirable features of algebras and coalgebras that have already been widely applied in theoretical computer science. Several of the elementary results in universal algebra and coalgebra up to the isomorphism theorems are proven here for dialgebras and hints are given as to how these more general results reduce to the two special cases.
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