Computational category theory paper - request for comments

Computational category theory paper - request for comments

[Shane O'Conchuir]

Hi all,

I've written a paper on computational category theory but have for a while been
unable to determine whether or not my methods or results are new. I would
greatly appreciate any input from the community on this matter.

The paper, "Proper Diagrams for Constructing Presheaf-Valued Limits", is about
the construction of limits of diagrams of presheaves. The content is not too
deep mathematically and is aimed more at computation. The basic idea is that
given a functor D from a small category C into a category of presheaves, I
construct a second functor D' of the same type where there is a natural
transformation D'->D whose components are monomorphisms. The construction has
the property that the limit of D is isomorphic to the limit of D'. The
intuition is that we remove parts of the presheaves so that the computation of
the limit is easier. I like to think of this approach as orthogonal to the use
of initial functors to construct limits. Both methods preserve the limit but
initial functors reduce the number of objects in the domain of a diagram
whereas our transformation reduces the objects in the codomain of the diagram.

A concise version of the paper is available at
https://www.cs.tcd.ie/Shane.OConchuir/limits/limitspaper.pdf
A draft technical report with the missing proofs and some appendices is
available at
https://www.cs.tcd.ie/Shane.OConchuir/limits/limitstr.pdf
The technical report explains how I derived my definition of "spare" element.

Any comments, corrections, criticisms, or references are welcome. In particular,
 I would like to know if any of this seems familiar (apologies in advance!)
Also, my choice of terminology ("proper", "inconsistent") probably conflicts
with normal use and one of my constructions, 'final proper diagram', may well
be called 'initial proper diagram'.


Many regards,

Shane O'Conchuir
Department of Computer Science
Trinity College Dublin