Title
Lax algebras via initial monad morphisms: APP, TOP, MET and ORDLax algebras via initial monad morphisms: APP, TOP, MET and ORD
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Analytical and topological structures
Fundamental Mathematics
Publication type
article
Publication
Amsterdam,
Subject
Mathematics
Source (journal)
Topology and its applications. - Amsterdam
Volume/pages
(2011)
ISSN
0166-8641
ISI
000289753900006
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper contributes to the algebraization of topology via the theory of monads and lax extensions of monads and their associated lax algebras (see Barr (1970) [1], Clementino and Hofmann (2003) [2], Clementino, Hofmann and Tholen (2004) [4], Clementino and Tholen (2003) [5], Lowen and Vroegrijk (2008) [11], Manes (1974) [12], Seal (2005) [14]). We construct a monad View the MathML source, a lax extension View the MathML source and monad morphisms into View the MathML source from the most important monads as studied in the aforementioned papers such that their lax extensions and their associated categories of lax algebras can be derived from the extension View the MathML source by initial lifts via these monad morphisms. This provides us with a completely unified way to obtain the categories View the MathML source, View the MathML source, View the MathML source and View the MathML source without the necessity to leave the realm of View the MathML source as was previously required in Clementino and Hofmann (2003) [2], Clementino, Hofmann and Tholen (2004) [4] and Clementino and Tholen (2003) [5] in particular in order to obtain View the MathML source and View the MathML source.
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