Mathematics – Category Theory
Scientific paper
2009-12-08
Mathematics
Category Theory
24 pages; v2: diverse revisions; v3: chopped about in face of trenchant and insightful referee feedback
Scientific paper
The notion of Grothendieck topos may be considered as a generalisation of that of topological space, one in which the points of the space may have non-trivial automorphisms. However, the analogy is not precise, since in a topological space, it is the points which have conceptual priority over the open sets, whereas in a topos it is the other way around. Hence a topos is more correctly regarded as a generalised locale, than as a generalised space. In this article we introduce the notion of ionad, which stands in the same relationship to a topological space as a (Grothendieck) topos does to a locale. We develop basic aspects of their theory and discuss their relationship with toposes.
No associations
LandOfFree
Ionads does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ionads, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ionads will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-385471