most recent 30 from http://mathoverflow.net 2013-05-24T07:15:16Z http://mathoverflow.net/feeds/question/18548 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18548/is-the-face-poset-a-heyting-algebra Mikael Vejdemo-Johansson 2010-03-18T06:11:34Z 2010-03-19T03:55:54Z

<p>Is the face poset of a simplicial or nice enough cellular complex a Heyting algebra in some natural way?</p> <p><em>Edited to add:</em> For the benefit of illustration, here's a few face posets:</p> <ul> <li><p>the boundary of a square: Elements $a,b,c,d$ of dimension 0 and $x,y,z,w$ of dimension 1; poset relations $a,b &lt; x$; $b,c &lt; y$; $c,d &lt; z$; $a,d &lt; w$.</p></li> <li><p>Two 2-simplices joined along a common edge: Elements $a,b,c,d$ of dimension 0, $j,k,l,m,n$ of dimension 1 and $x,y$ of dimension 2. Poset relations are: $a,b &lt; j$; $a,c &lt; k$; $b,c &lt; l$; $b, d &lt; m$; $c,d &lt; n$ and $j,k,l &lt; x$ and $l,m,n &lt; y$.</p></li> </ul>