Is the face poset a Heyting algebra? - MathOverflow 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 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>