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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeOct 26th 2010
   • (edited Oct 26th 2010)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAs I need trees as relational structures for my modal logic stuff, I have added something on them in [[tree]]. I took this from of the definition from Blackburn et al, and it seems to me to be related to the previous paragraph in [[tree]]. Any thoughts? I am not 100% happy with my addition as there seem to be some awkwardness in their formulation. I am trying to go towards a n-dim analogue of modal stuff, and [[tree|here]] the relation $S$ has properties that state that its converse relation $S^{op}$ is a partial function with domain the set of nodes minus the root. Looking at this homotopically it says that $S^{op}$ forms part of a contracting homotopy. This in turn suggests that there is a perhaps useful n-relational structure obtained from an n-dim contractible complex (generalising a converse to simple homotopy operations). Has anyone come on something like this explicitly? The idea is a fairly elementary one to have but a nPOV type development might be fun at least.

   As I need trees as relational structures for my modal logic stuff, I have added something on them in tree. I took this from of the definition from Blackburn et al, and it seems to me to be related to the previous paragraph in tree. Any thoughts? I am not 100% happy with my addition as there seem to be some awkwardness in their formulation.

   I am trying to go towards a n-dim analogue of modal stuff, and here the relation $S$ has properties that state that its converse relation $S^{op}$ is a partial function with domain the set of nodes minus the root. Looking at this homotopically it says that $S^{op}$ forms part of a contracting homotopy. This in turn suggests that there is a perhaps useful n-relational structure obtained from an n-dim contractible complex (generalising a converse to simple homotopy operations). Has anyone come on something like this explicitly? The idea is a fairly elementary one to have but a nPOV type development might be fun at least.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 17th 2016
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI added to [[tree]] a new subsection, outlining some of Joachim Kock's point of view on the relation between trees and [[polynomial endofunctors]]. (I had an inkling this would be somewhat relevant to the recent additions by Jon Beardsley on generalized graphs, etc., which is what instigated this addition.) There's a quick gloss on a double category which I didn't check too carefully.

   I added to tree a new subsection, outlining some of Joachim Kock’s point of view on the relation between trees and polynomial endofunctors. (I had an inkling this would be somewhat relevant to the recent additions by Jon Beardsley on generalized graphs, etc., which is what instigated this addition.) There’s a quick gloss on a double category which I didn’t check too carefully.