A directed loop graph may be understood as a thin (0,1)-directed pseudograph, hence as a thin directed pseudograph enriched over the cartesian monoidal poset of truth values. In generalization, one may speak of enriching directed loop graphs over other monoidal posets.
Let be a monoidal poset, such as a meet-semilattice. A -enriched directed loop graph or directed loop graph enriched over/in is a set with a binary function
An ordinary directed loop graph is just an -enriched directed loop graph, with the set of truth values.
A Lawvere metric space is a -enriched proset, where are the non-negative Dedekind real numbers.
A quasipseudometric space is a -enriched proset, where are the non-negative Dedekind real numbers.
A pseudometric space is a -enriched symmetric proset, where are the non-negative Dedekind real numbers.
A metric space is a -enriched set, where are the non-negative Dedekind real numbers.
Last revised on September 22, 2022 at 18:40:33. See the history of this page for a list of all contributions to it.