Geodesic
Composition-Representative Subsets
Theory and applications of categories, Tome 11 (2003), pp. 420-437.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

A specific property applicable to subsets of a hom-set in any small category is defined. Subsets with this property are called composition-representative. The notion of composition-representability is motivated both by the representability of a linear functional on an associative algebra, and, by the recognizability of a subset of a monoid. Various characterizations are provided which therefore may be regarded as analogs of certain characterizations for representability and recognizablity. As an application, the special case of an algebraic theory T is considered and simple characterizations for a recognizable forest are given. In particular, it is shown that the composition-representative subsets of the hom-set T([1],[0]), the set of all trees, are the recognizable forests and that they, in turn, are characterized by a corresponding finite `syntactic congruence.' Using a decomposition result (proved here), the composition-representative subsets of the hom-set T([m],[0]), (0 \leq m) are shown to be finite unions of m-fold (cartesian) products of recognizable forests.
Classification : 18B99, 18C99, 08A62, 08A70
Keywords: recognizable language, recognizable forest, representative functional, syntactic congruence, algebraic theory, translates 
@article{TAC_2003_11_a18,
     author = {Gary Griffing},
     title = {Composition-Representative {Subsets}},
     journal = {Theory and applications of categories},
     pages = {420--437},
     publisher = {mathdoc},
     volume = {11},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2003_11_a18/}
}
TY  - JOUR
AU  - Gary Griffing
TI  - Composition-Representative Subsets
JO  - Theory and applications of categories
PY  - 2003
SP  - 420
EP  - 437
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2003_11_a18/
LA  - en
ID  - TAC_2003_11_a18
ER  - 
%0 Journal Article
%A Gary Griffing
%T Composition-Representative Subsets
%J Theory and applications of categories
%D 2003
%P 420-437
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2003_11_a18/
%G en
%F TAC_2003_11_a18
Gary Griffing. Composition-Representative Subsets. Theory and applications of categories, Tome 11 (2003), pp. 420-437. http://geodesic.mathdoc.fr/item/TAC_2003_11_a18/