MyWikiBiz, Author Your Legacy — Friday May 03, 2024
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, 04:06, 29 March 2009
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| ===Category 2=== | | ===Category 2=== |
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− | <pre> | + | {| align="center" cellpadding="8" width="90%" <!--QUOTE--> |
− | | A 'category' is a deductive system in which
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− | | the following equations hold between proofs:
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| | | | | |
− | | E1. f 1_A = f, | + | <p>A ''category'' is a deductive system in which the following equations hold between proofs:</p> |
| + | |- |
| | | | | |
− | | 1_B f = f,
| + | <p><math>\begin{array}{ll} |
| + | \text{E1.} & f 1_A = f, \qquad 1_B f = f, \qquad (hg)f = h(gf), |
| + | \\[8pt] |
| + | & \text{for all}~ f : A \to B, \quad g : B \to C, \quad h : C \to D. |
| + | \end{array}</math></p> |
| + | |- |
| | | | | |
− | | (hg)f = h(gf),
| + | <p>(Lambek & Scott, 52). |
− | | | + | |} |
− | | for all f : A -> B, g : B -> C, h : C -> D.
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− | </pre>
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| | | |
| ===Cartesian Category=== | | ===Cartesian Category=== |