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Directory:Jon Awbrey/Papers/Propositions As Types (view source)
Revision as of 14:14, 27 March 2009
, 14:14, 27 March 2009→Graph (Review): markup
===Graph (Review)===
===Graph (Review)===
<pre>
{| align="center" cellpadding="8" width="90%" <!--QUOTE-->
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<p>We recall … that, for categories, a ''graph'' consists of two classes and two mappings between them:</p>
<center><pre>
o--------------o source o--------------o
| | ----------------> | |
| Arrows | | Objects |
| | ----------------> | |
o--------------o target o--------------o
</pre></center>
<p>In graph theory the arrows are usually called ''oriented edges'' and the objects ''nodes'' or ''vertices'', but in various branches of mathematics other words may be used. Instead of writing</p>
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::<p><math>\operatorname{source}(f) = A, \quad \operatorname{target}(f) = B,</math></p>
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| of mathematics other words may be used. Instead of writing
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<p>one often writes <math>f : A \to B</math> or <math>A \xrightarrow{~f~} B.</math> We shall look at graphs with additional structure which are of interest in logic.</p>
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</pre>
===Deductive System===
===Deductive System===