The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
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The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, the definition of monad began to appear extensively in theoretic...
متن کاملCategory Theoretic Understandings of Universal Algebra and its Dual: Monads and Lawvere Theories, Comonads and What?
Universal algebra is often known within computer science in the guise of algebraic specification or equational logic. In 1963, it was given a category theoretic characterisation in terms of what are now called Lawvere theories. Unlike operations and equations, a Lawvere theory is uniquely determined by its category of models. Except for a caveat about nullary operations, the notion of Lawvere t...
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Names, or object-level variables, are a ubiquitous feature in programming languages and other computational applications. Reasoning with names, and related constructs like binding and freshness, often poses conceptual and technical challenges. Nominal Equational Logic (NEL) is a logic for reasoning about equations in the presence of freshness side conditions. This paper gives a category theoret...
متن کاملElectronic Notes in Theoretical Computer Science Mathematical Foundations of Programming Semantics
Universal algebra is often known within computer science in the guise of algebraic specification or equational logic. In 1963, it was given a category theoretic characterisation in terms of what are now called Lawvere theories. Unlike operations and equations, a Lawvere theory is uniquely determined by its category of models. Except for a caveat about nullary operations, the notion of Lawvere t...
متن کاملNominal Lawvere Theories
Lawvere theories provide a category theoretic view of equational logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the “fres...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2007
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2007.02.019