% This file: http://angg.twu.net/LATEX/2014sfc-abstract.tex
%                         (find-LATEX "2014sfc-abstract.tex")
% See also:  http://angg.twu.net/math-b.html#sheaves-for-children
%                      (find-TH "math-b"    "sheaves-for-children")
% This is the 1-page abstract that I submitted to EBL2014 on 2014feb10.
% Eduardo Ochs

\documentclass{ebl}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{hyperref}

% (find-angg "sheavesforchildren/abstract/")
% (find-angg "sheavesforchildren/abstract/ochs-abstract.tex")
% (find-sh "latex    2014sfc-abstract.tex")
% (find-xdvipage    "2014sfc-abstract.dvi")
% (find-sh "pdflatex 2014sfc-abstract.tex")
% (find-xpdfpage    "2014sfc-abstract.pdf")

% Use this command to insert the title of your work.
\title{Sheaves for Children}

% Use this command to insert authors names and identify the affiliations.
% After each author insert a \inst{} with a number to identify the institution.
% Authors with the same affiliation must have the same number.
\author{Eduardo Ochs\inst{1}}

% Use this command to insert the affiliation details.
% To break lines use \\
% After an institute if you need to insert an other institute use the
% command \nextinstitute inside the \institute{}.
% To insert the email of each author use the command \email{} inside
% the \institute{}.
\institute{
  % LLaRC -- Laborat\'orio de L\'ogica e Representa\c c\~ao do Conhecimento \\
  Departamento de F\'\i sica e Matem\'atica \\
  P\'olo Universit\'ario de Rio das Ostras \\
  Universidade Federal Fluminense
  \email{eduardoochs@gmail.com} \\
  \url{http://angg.twu.net/math-b.html\#sfc}
}

% (find-dn4exfile "edrxdefs.tex")

\def\Set{\mathbf{Set}}
\def\N{\mathbb{N}}
\def\catD{\mathbf{D}}

\begin{document}

% This command is mandatory to generate the headers of your work.
\maketitle

First-year university students -- the ``children'' of the title --
often prefer to start from an interesting particular case, and only
then proceed to general statements. How can we make intuitionistic
logic, toposes, and sheaves accessible to them?

Let $D$ be a finite subset of $\N^2$. Draw arrows for all the ``black
pawns moves'' between points of $D$, and let $\catD$ be the poset
generated by that graph; $\catD$ is what we call a ``ZDAG'', and
$\Set^\catD$ is a ``ZDAG-topos''. It turns out that the truth-values
of a $\Set^\catD$ can be represented in a very nice way as
two-dimensional ASCII diagrams, and that all the operations leading to
sheaves and geometric morphisms can be understood via algorithms on
diagrams.

In this talk we will present a computer library for performing
computations interactively on the truth-values of ZDAG-toposes. The
diagrams are rendered in ASCII by default, but there is a module that
typesets them in \LaTeX.


\end{document}
