Dualizing Clones as Models of Lawvere Theories
نویسندگان
چکیده
منابع مشابه
Nominal 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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Countable Lawvere theories model computational effects such as exceptions, side-effects, interactive input/output, nondeterminism and probabilistic nondeterminism. The category of countable Lawvere theories has sums, tensors, and distributive tensors, modelling natural combinations of such effects. It is also closed under taking images. Enrichment in a category such as Cpo allows one to extend ...
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Many term calculi, like λ-calculus or π-calculus, involve binders for names, and the mathematics of bound variable names is subtle. Schönfinkel introduced the SKI combinator calculus in 1924 to clarify the role of quantified variables in intuitionistic logic by eliminating them. Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchronous π-calculus, bu...
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Lawvere theories provide a categorical formulation of the algebraic theories from universal algebra. Freyd categories are categorical models of first-order effectful programming languages. The notion of sound limit doctrine has been used to classify accessible categories. We provide a definition of Lawvere theory that is enriched in a closed category that is locally presentable with respect to ...
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PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category, but whereas PROPs are symmetric monoidal, Lawvere categories are cartesian. This paper formulates the connection between the two notions using Lack’s technique for composing PROPs via distributive laws. We show Lawvere categories can be seen as resulting from a distrib...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2014
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2014.02.005