Subject: excision and n-cubes From: "Ronnie Brown" Date: Mon, 24 Jul 2006 16:47:38 +0100 What I wrote on excision got too abbreviated! Of course an n-cube in a category C may be regarded as a map of (n-1)-cubes. However there is a functor from (r-cubes in C) to (r-cubes of r-cubes in C). To see an example, a square C A B X becomes a square of squares CC CA CC CA CC CA BB BX and a pushout square becomes a pushout of squares of squares. This is useful if you are given a functor \Pi: (squares) \to (some algebra). So the excision map for an n-cube becomes a map of (n-1)-cubes of (n-1)-cubes, or an n-cube of (n-1)-cubes! Ronnie Brown www.bangor.ac.uk/r.brown