## Metagories. (arXiv:1810.08828v1 [math.CT])

Metagories are metrically enriched directed multigraphs with designated loops. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the distance of a pair of consecutive arrows to any potential candidate for their composite. These values may live in an arbitrary commutative quantale. Generalizing and extending recent work by Aliouche and Simpson, we give a condition for the existence of an Yoneda-type embedding which, in particular, gives the isometric embeddability of a metagory into a metrically enriched category. The generality of the value quantale allows for applications beyond the classical metric context.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Metagories are metrically enriched directed multigraphs with designated loops. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the distance of a pair of consecutive arrows to any potential candidate for their composite. These values may live in an arbitrary commutative quantale. Generalizing and extending recent work by Aliouche and Simpson, we give a condition for the existence of an Yoneda-type embedding which, in particular, gives the isometric embeddability of a metagory into a metrically enriched category. The generality of the value quantale allows for applications beyond the classical metric context.