On The Continuous Category in A Topos

DOI

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.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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