Proceedings of the 2014 International Conference on Mechatronics, Control and Electronic Engineering

On The Continuous Category in A Topos

Authors
Tao Lu, Zhenzhen Zhu
Corresponding Author
Tao Lu
Available Online March 2014.
DOI
https://doi.org/10.2991/mce-14.2014.60How to use a DOI?
Keywords
coproduct; category; continuous;relation;topos
Abstract
The way-below relation defined on dcpos is a important concept, it is the basis for the continuity of dcpos. And a poset is also a category, so we want to generalize the concept of way-below to category and further define continous category. In this paper, we give the way-below relation on arbitrary small categories and even a topos and introduce the concept of continuous category and obtain some correspontive characterizations by mean of the diagram proof. This also shows diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.
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Proceedings
2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14)
Part of series
Advances in Intelligent Systems Research
Publication Date
March 2014
ISBN
978-94-62520-31-8
ISSN
1951-6851
DOI
https://doi.org/10.2991/mce-14.2014.60How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Tao Lu
AU  - Zhenzhen Zhu
PY  - 2014/03
DA  - 2014/03
TI  - On The Continuous Category in A Topos
BT  - 2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14)
PB  - Atlantis Press
SP  - 274
EP  - 277
SN  - 1951-6851
UR  - https://doi.org/10.2991/mce-14.2014.60
DO  - https://doi.org/10.2991/mce-14.2014.60
ID  - Lu2014/03
ER  -