(0,1)-category

(0,1)-topos

Contents

Idea

Following the general concept of $(n,r)$-category, a $(0,1)$-category is (up to equivalence) a poset or (up to isomorphism) a proset. We may also call this a $1$-poset.

Definition

Definition

An (n,1)-category is an (∞,1)-category such that every hom ∞-groupoid is (n-1)-truncated.

Notice that

Proposition

An $(0,1)$-category is equivalently a poset.

Proof

We may without restriction assume that every hom-$\infty$-groupoid is in fact a set on the nose. Then since this is (-1)-truncated it is either empty or the singleton. So there is at most one morphism from any object to any other.

Extra stuff, structure, property

Revised on March 15, 2012 15:36:09 by Urs Schreiber (82.172.178.200)