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% 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}