On The Continuous Category in A Topos
Tao Lu, Zhenzhen Zhu
Available Online March 2014.
- https://doi.org/10.2991/mce-14.2014.60How to use a DOI?
- coproduct; category; continuous;relation;topos
- 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.
- 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 -