A model of a Lawvere theory in a category C with finite products is a finite-product preserving functor M : L → C. A morphism of modelsh : M → N where M and N are models of L is a natural transformation of functors.
Category of Lawvere theoriesedit
A map between Lawvere theories (L, I) and (L′, I′) is a finite-product preserving functor that commutes with I and I′. Such a map is commonly seen as an interpretation of (L, I) in (L′, I′).
Lawvere theories together with maps between them form the category Law.
Variationsedit
Variations include multisorted (or multityped) Lawvere theory, infinitary Lawvere theory, and finite-product theory.[1]
Hyland, Martin; Power, John (2007), "The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads" (PDF), Electronic Notes in Theoretical Computer Science, 172 (Computation, Meaning, and Logic: Articles dedicated to Gordon Plotkin): 437–458, CiteSeerX10.1.1.158.5440, doi:10.1016/j.entcs.2007.02.019
Lawvere, William F. (1963), "Functorial Semantics of Algebraic Theories", PhD Thesis, vol. 50, no. 5, Columbia University, pp. 869–872, Bibcode:1963PNAS...50..869L, doi:10.1073/pnas.50.5.869, PMC221940, PMID 16591125
January 01, 1970
lawvere, theory, category, theory, named, after, american, mathematician, william, lawvere, category, that, considered, categorical, counterpart, notion, equational, theory, contents, definition, category, lawvere, theories, variations, also, notes, references. In category theory a Lawvere theory named after American mathematician William Lawvere is a category that can be considered a categorical counterpart of the notion of an equational theory Contents 1 Definition 2 Category of Lawvere theories 3 Variations 4 See also 5 Notes 6 ReferencesDefinition editLet ℵ 0 displaystyle aleph 0 nbsp be a skeleton of the category FinSet of finite sets and functions Formally a Lawvere theory consists of a small category L with strictly associative finite products and a strict identity on objects functor I ℵ 0 op L displaystyle I aleph 0 text op rightarrow L nbsp preserving finite products A model of a Lawvere theory in a category C with finite products is a finite product preserving functor M L C A morphism of models h M N where M and N are models of L is a natural transformation of functors Category of Lawvere theories editA map between Lawvere theories L I and L I is a finite product preserving functor that commutes with I and I Such a map is commonly seen as an interpretation of L I in L I Lawvere theories together with maps between them form the category Law Variations editVariations include multisorted or multityped Lawvere theory infinitary Lawvere theory and finite product theory 1 See also editAlgebraic theory Clone algebra Monad category theory Notes edit Lawvere theory at the nLabReferences editHyland Martin Power John 2007 The Category Theoretic Understanding of Universal Algebra Lawvere Theories and Monads PDF Electronic Notes in Theoretical Computer Science 172 Computation Meaning and Logic Articles dedicated to Gordon Plotkin 437 458 CiteSeerX 10 1 1 158 5440 doi 10 1016 j entcs 2007 02 019 Lawvere William F 1963 Functorial Semantics of Algebraic Theories PhD Thesis vol 50 no 5 Columbia University pp 869 872 Bibcode 1963PNAS 50 869L doi 10 1073 pnas 50 5 869 PMC 221940 PMID 16591125 Retrieved from https en wikipedia org w index php title Lawvere theory amp oldid 1110881349, wikipedia, wiki, book, books, library,
