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 $(M, \leq, \wedge, \top)$ be a monoidal poset, such as a meet-semilattice. A $M$-enriched directed loop graph or directed loop graph enriched over/in $M$ is a set $P$ with a binary function $o:P \times P \to M$
An ordinary directed loop graph is just an $\Omega$-enriched directed loop graph, with $\Omega$ the set of truth values.
A Lawvere metric space is a $\overline{\mathbb{R}_{\geq 0}}$-enriched proset, where $\mathbb{R}_{\geq 0}$ are the non-negative Dedekind real numbers.
A quasipseudometric space is a $\mathbb{R}_{\geq 0}$-enriched proset, where $\mathbb{R}_{\geq 0}$ are the non-negative Dedekind real numbers.
A pseudometric space is a $\mathbb{R}_{\geq 0}$-enriched setoid, where $\mathbb{R}_{\geq 0}$ are the non-negative Dedekind real numbers.
Created on May 30, 2022 at 09:57:07. See the history of this page for a list of all contributions to it.