Order-enriched solid functors

Lurdes Sousa; Walter Tholen

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 4, page 553-580
  • ISSN: 0010-2628

Abstract

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Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behaviour with respect to specific weighted (co)limits, and on the presentation of examples, which include functors of general varieties of ordered algebras and special ones, such as ordered vector spaces.

How to cite

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Sousa, Lurdes, and Tholen, Walter. "Order-enriched solid functors." Commentationes Mathematicae Universitatis Carolinae 60.4 (2019): 553-580. <http://eudml.org/doc/295079>.

@article{Sousa2019,
abstract = {Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behaviour with respect to specific weighted (co)limits, and on the presentation of examples, which include functors of general varieties of ordered algebras and special ones, such as ordered vector spaces.},
author = {Sousa, Lurdes, Tholen, Walter},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ordered category; (strongly) order-solid functor; weighted (co)limit; ordered algebra},
language = {eng},
number = {4},
pages = {553-580},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Order-enriched solid functors},
url = {http://eudml.org/doc/295079},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Sousa, Lurdes
AU - Tholen, Walter
TI - Order-enriched solid functors
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 4
SP - 553
EP - 580
AB - Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behaviour with respect to specific weighted (co)limits, and on the presentation of examples, which include functors of general varieties of ordered algebras and special ones, such as ordered vector spaces.
LA - eng
KW - ordered category; (strongly) order-solid functor; weighted (co)limit; ordered algebra
UR - http://eudml.org/doc/295079
ER -

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