Linton's theorem, in category theory, concerns the correspondence between monads and Lawvere theories, the two principal category theoretic formulations of universal algebra. The correspondence was essentially introduced in Linton's own 1969 work, though later authors, notably Eduardo Dubuc, gave the first fully explicit statements and proofs of parts of the result, extending it to the more general setting of enriched categories.
Facts
StatementThe category of finitary monads on Set is equivalent to the category of Lawvere theories and, subject to a generalization in the definition of Lawvere theory, every monad arises thus, uniquely up to coherent isomorphism. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Linton's theorem (equational theory), Wikipedia
Source Linton's theorem (equational theory), Wikipedia
Sources
1. Linton's theorem (equational theory), Wikipedia
Section on the theorems relating monads and Lawvere theories due to Linton
The category of finitary monads on Set is equivalent to the category of Lawvere theories and, subject to a generalization in the definition of Lawvere theory, every monad arises thus, uniquely up to coherent isomorphism.
Opening paragraph, before the theorem statements
Although these results are not explicitly stated, they were essentially introduced by Linton (1969).
In Branch: Universal Algebra, Lead paragraph
These two notions are the two main category theoretic formulations of universal algebra.
In Branch: Category Theory, Lead paragraph
These two notions are the two main category theoretic formulations of universal algebra.
In Group: General and Universal Algebra, Lead section
are the two main category theoretic formulations of universal algebra. Although these results are not explicitly stated
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.