A duality between infinitary varieties and algebraic theories

Adámek, Jiří, Koubek, Václav, and Velebil, Jiří. "A duality between infinitary varieties and algebraic theories." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 529-541. <http://eudml.org/doc/248619>.

@article{Adámek2000,
abstract = {A duality between $\lambda $-ary varieties and $\lambda $-ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal $\lambda $, whenever $\lambda $-small products commute with $\mathcal \{D\}$-colimits in $\text\{Set\}$, then $\mathcal \{D\}$ must be a $\lambda $-filtered category. We nevertheless introduce the concept of $\lambda $-sifted colimits so that morphisms between $\lambda $-ary varieties (defined to be $\lambda $-ary, regular right adjoints) are precisely the functors preserving limits and $\lambda $-sifted colimits.},
author = {Adámek, Jiří, Koubek, Václav, Velebil, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {variety; Lawvere theory; sifted colimit; filtered colimit; varieties; diagrams; limits},
language = {eng},
number = {3},
pages = {529-541},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A duality between infinitary varieties and algebraic theories},
url = {http://eudml.org/doc/248619},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Adámek, Jiří
AU - Koubek, Václav
AU - Velebil, Jiří
TI - A duality between infinitary varieties and algebraic theories
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 529
EP - 541
AB - A duality between $\lambda $-ary varieties and $\lambda $-ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal $\lambda $, whenever $\lambda $-small products commute with $\mathcal {D}$-colimits in $\text{Set}$, then $\mathcal {D}$ must be a $\lambda $-filtered category. We nevertheless introduce the concept of $\lambda $-sifted colimits so that morphisms between $\lambda $-ary varieties (defined to be $\lambda $-ary, regular right adjoints) are precisely the functors preserving limits and $\lambda $-sifted colimits.
LA - eng
KW - variety; Lawvere theory; sifted colimit; filtered colimit; varieties; diagrams; limits
UR - http://eudml.org/doc/248619
ER -