Contents

(0,1)-category

(0,1)-topos

# Contents

## Idea

Recall (here) that a preorder may be understood as a thin (0,1)-category, hence as a thin category enriched over the cartesian monoidal proset of truth values. In generalization, one may speak of enriching preorders over other monoidal posets.

## Defintion

Let $(M, \leq, \wedge, \top)$ be a monoidal poset. A $M$-enriched proset or proset enriched over/in $M$ is a set $P$ with a binary function $o:P \times P \to M$ such that

• for every $a \in P$, $b \in P$, and $c \in P$, $o(a, b) \wedge o(b, c) \leq o(a, c)$

• for every $a \in P$, $\top \leq o(a, a)$.

## See also

Last revised on September 22, 2022 at 14:40:57. See the history of this page for a list of all contributions to it.