Gaps and dualities in Heyting categories

Jaroslav Nešetřil; Aleš Pultr; Claude Tardif

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 9-23
  • ISSN: 0010-2628

Abstract

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We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.

How to cite

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Nešetřil, Jaroslav, Pultr, Aleš, and Tardif, Claude. "Gaps and dualities in Heyting categories." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 9-23. <http://eudml.org/doc/250193>.

@article{Nešetřil2007,
abstract = {We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.},
author = {Nešetřil, Jaroslav, Pultr, Aleš, Tardif, Claude},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Heyting algebras; dualities and gaps; Heyting categories; Heyting categories; Heyting algebras; dualities; gaps; Cartesian closed categories},
language = {eng},
number = {1},
pages = {9-23},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Gaps and dualities in Heyting categories},
url = {http://eudml.org/doc/250193},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Nešetřil, Jaroslav
AU - Pultr, Aleš
AU - Tardif, Claude
TI - Gaps and dualities in Heyting categories
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 9
EP - 23
AB - We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
LA - eng
KW - Heyting algebras; dualities and gaps; Heyting categories; Heyting categories; Heyting algebras; dualities; gaps; Cartesian closed categories
UR - http://eudml.org/doc/250193
ER -

References

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  12. Nešetřil J., Pultr A., On classes of relations and graphs determined by subobjects and factorobjects, Discrete Math. 22 (1978), 287-300. (1978) MR0522724
  13. Nešetřil J., Tardif C., Density via duality, Theoret. Comput. Sci. 287 2 (2002), 585-595. (2002) Zbl1058.05062MR1930237
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