Premium
Precovers, Modalities and Universal Closure Operators in a Topos
Author(s) -
Bell John L.,
Gebellato Silvia
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420124
Subject(s) - topos theory , closure (psychology) , mathematics , modalities , set (abstract data type) , relation (database) , modality (human–computer interaction) , pure mathematics , closure operator , mathematics subject classification , discrete mathematics , algebra over a field , closed set , computer science , artificial intelligence , data mining , programming language , market economy , art , social science , literature , sociology , economics
In this paper we develop the notion of formal precover in a topos by defining a relation between elements and sets in a local set theory. We show that such relations are equivalent to modalities and to universal closure operators. Finally we prove that these relations are well characterized by a convenient restriction to a particular set. Mathematics Subject Classification: 03G30, 03B20, 03F55.