Paths and cylinders
Zigzags of morphisms
In a category a zigzag of morphisms is a finite collection of morphisms in of the form
A zigzag consisting just out of two morphisms is a roof or span.
General such zig-zags of morphisms represent ordinary morphisms in the groupoidification of – the Kan fibrant replacement of its nerve, its simplicial localization or its 1-categorical localization at all its morphisms.
More generally, if in these zig-zags the left-pointing morphisms are restricted to be in a class , then these zig-zags represent morphisms in the simplicial localizaton or localization of at .
Revised on August 26, 2012 18:33:13
by Urs Schreiber