MyWikiBiz, Author Your Legacy — Sunday April 28, 2024
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, 14:14, 27 March 2009
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Line 2,351: |
| ===Graph (Review)=== | | ===Graph (Review)=== |
| | | |
− | <pre> | + | {| align="center" cellpadding="8" width="90%" <!--QUOTE--> |
− | | We recall (Part 0, Definition 1.2) that, for categories,
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− | | a 'graph' consists of two classes and two mappings
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− | | between them:
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| | | | | |
− | | o--------------o source o--------------o
| + | <p>We recall … that, for categories, a ''graph'' consists of two classes and two mappings between them:</p> |
− | | | | ----------------> | |
| + | |
− | | | Arrows | | Objects |
| + | <center><pre> |
− | | | | ----------------> | |
| + | |
− | | o--------------o target o--------------o
| + | 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> |
| + | |- |
| | | | | |
− | | In graph theory the arrows are usually called "oriented edges"
| + | ::<p><math>\operatorname{source}(f) = A, \quad \operatorname{target}(f) = B,</math></p> |
− | | and the objects "nodes" or "vertices", but in various branches
| + | |- |
− | | of mathematics other words may be used. Instead of writing | |
| | | | | |
− | | source(f) = A,
| + | <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> |
− | |
| + | |} |
− | | target(f) = B,
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− | | f
| |
− | | one often writes f : A -> B or A ---> B. We shall
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− | | look at graphs with additional structure which are
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− | | of interest in logic.
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− | </pre> | |
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| ===Deductive System=== | | ===Deductive System=== |