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% Eduardo Ochs
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\title{Sheaves for Children}
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\author{Eduardo Ochs\inst{1}}
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% 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}
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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}