nLab r-reversible n-poset

Idea

Just as an $(\infinity,r)$-category could be $n$-connected, orthogonal to $n$-truncated $(\infinity,r)$-categories, which are just $(n,r)$-categories, an $(n,\infty)$-category, or $(n+1)$-poset, could be $r$-reversible, which are orthogonal to $r$-directed $(n+1)$-posets, which are just $(n,r)$-categories.

Definition

An $n$-poset is $r$-reversible if any $k$-morphism for $k \leq r$ is reversible. You may interpret this definition as weakly or strictly as you like, by starting with weak or strict notions of $n$-poset.

Examples

• A $0$-reversible $n$-poset is just a $n$-poset.

• A $n$-reversible $(n+1)$-poset is a $n$-groupoid.

See also

• (n,r)-category

• k-simply connected n-category