منابع مشابه
Universal coalgebra: a theory of systems
In the semantics of programming, nite data types such as nite lists, have traditionally been modelled by initial algebras. Later nal coalgebras were used in order to deal with in nite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property ...
متن کاملUniversal Dialgebra: Unifying Universal Algebra and Coalgebra
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...
متن کاملCoalgebra Gauge Theory
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory, embeddable quantum homogeneous spaces and braided group gauge theory, the latter being introduced now by these means. Examples include ones in which the gauge groups...
متن کاملA Brief Introduction to Coalgebra Representation Theory
In this survey, we review fundamental properties of coalgebras and their representation theory. Following J.A. Green we present the block theory of coalgebras using indecomposable injectives comodules. Using the cohom and cotensor functors we state Takeuchi-Morita equivalence and use it to sketch the proof of existence of “basic” coalgebras, due to the author and S. Montgomery. This leads to a ...
متن کاملA Concrete Final Coalgebra Theorem for ZF Set Theory
A special final coalgebra theorem, in the style of Aczel’s [2], is proved within standard Zermelo-Fraenkel set theory. Aczel’s AntiFoundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s Solution and Substitution Lemmas ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2000
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00056-6