Lawvere completeness in Topology

Details Lawvere completeness in Topology Lawvere completeness in Topology

2007-04-30

arxiv.org/abs/0704.3976v1

Mathematics

Category Theory

Scientific paper

It is known since 1973 that Lawvere's notion of (Cauchy-)complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper we introduce the corresponding notion of Lawvere completeness for $(\mathbb{T},\mathsf{V})$-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones means weak sobriety while for the latter means Cauchy completeness. Further, we show that $\mathsf{V}$ has a canonical $(\mathbb{T},\mathsf{V})$-category structure which plays a key role: it is Lawvere-complete under reasonable conditions on the setting; permits us to define a Yoneda embedding in the realm of $(\mathbb{T},\mathsf{V})$-categories.

Affiliated with

Also associated with

No associations

Rating

Lawvere completeness in Topology 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 Lawvere completeness in Topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lawvere completeness in Topology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-415634