Algebraic methods in semantics
Information and Computation
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Categories of relational structures
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
An inductive view of graph transformation
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Normal Forms for Partitions and Relations
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
A View on Implementing Processes: Categories of Circuits
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
Equational Reasoning with Two-Dimensional Diagrams
Term Rewriting, French Spring School of Theoretical Computer Science, Advanced Course
Rewriting on cyclic structures
Rewriting on cyclic structures
Normal Forms for Partitions and Relations
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
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Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature σ as cartesian functors from the algebraic theory of σ, Th(σ), to Set. The functors we introduce are based on variations of the notion of theory, having a structure weaker than cartesian, and their target is Rel, the category of sets and relations. We argue that this functorial presentation provides an original abstract syntax for partial and multi-algebras.