Line 6,960:
Line 6,960:
</font><br>
</font><br>
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<pre>
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<br>
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o o
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<p>[[Image:Diff Log Dyn Sys -- Figure 70-a -- Tangent Functor Diagram.gif|center]]</p>
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/ \ / \
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<p><center><font size="+1">'''Figure 70-a. Tangent Functor Diagram for F‹u, v› = ‹((u)(v)), ((u, v))›'''</font></center></p>
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/ \ / \
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/ \ / O \
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/ \ o /@\ o
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/ \ / \ / \
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/ \ / \ / \
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/ O \ / O \ / O \
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o /@\ o o /@\ o /@\ o
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/ \ / \ / \ \ / \ \ / \
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/ \ / \ / \ / \ / \
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/ \ / \ / O \ / O \ / O \
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/ \ / \ o /@ o /@\ o /@ o
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/ \ / \ / \ \ / \ / \ \ / \
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/ \ / \ / \ / \ / \ / \
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/ O \ / O \ / O \ / O \ / O \ / O \
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o /@ o /@ o o /@ o /@ o /@ o /@ o
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|\ / \ /| |\ / \ / / \ / / \ /|
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| \ / \ / | | \ / \ / \ / \ / |
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| \ / \ / | | \ / O \ / O \ / O \ / |
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| \ / \ / | | o /@ o @\ o /@ o |
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| \ / \ / | | |\ / \ / \ / \ / \ /| |
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| \ / \ / | | | \ / \ / \ / | |
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| u \ / O \ / v | | u | \ / O \ / O \ / | v |
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o-------o @\ o-------o o---+---o @\ o @\ o---+---o
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\ / | \ / \ / \ / \ / |
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\ / | \ / \ / |
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\ / | du \ / O \ / dv |
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\ / o-------o @\ o-------o
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\ / \ /
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\ / \ /
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\ / \ /
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o o
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U% $T$ $E$U%
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o------------------>o
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| |
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| |
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| |
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| |
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F | | $T$F
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| |
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| |
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| |
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v v
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o------------------>o
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X% $T$ $E$X%
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o o
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/ \ / \
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/ \ / \
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/ \ / O \
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/ \ o /@\ o
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/ \ / \ / \
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/ \ / \ / \
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/ O \ / O \ / O \
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o /@\ o o /@\ o /@\ o
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/ \ / \ / \ \ / \ / / \
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/ \ / \ / \ / \ / \
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/ \ / \ / O \ / O \ / O \
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/ \ / \ o /@ o /@\ o @\ o
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/ \ / \ / \ \ / \ / \ / \ / / \
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/ \ / \ / \ / \ / \ / \
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/ O \ / O \ / O \ / O \ / O \ / O \
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o /@ o @\ o o /@ o /@ o @\ o @\ o
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|\ / \ /| |\ / \ / \ / \ / \ / \ /|
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| \ / \ / | | \ / \ / \ / \ / |
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| \ / \ / | | \ / O \ / O \ / O \ / |
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| \ / \ / | | o /@ o @ o @\ o |
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| \ / \ / | | |\ / / \ / \ / \ \ /| |
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| \ / \ / | | | \ / \ / \ / | |
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| x \ / O \ / y | | x | \ / O \ / O \ / | y |
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o-------o @ o-------o o---+---o @ o @ o---+---o
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\ / | \ / / \ \ / |
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\ / | \ / \ / |
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\ / | dx \ / O \ / dy |
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\ / o-------o @ o-------o
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\ / \ /
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\ / \ /
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\ / \ /
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o o
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Figure 70-a. Tangent Functor Diagram for F<u, v> = <((u)(v)), ((u, v))>
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</pre>
Figure 70-b shows another way to picture the action of the tangent functor on the logical transformation ''F''‹''u'', ''v''› = ‹((''u'')(''v'')), ((''u'', ''v''))›, roughly in the style of the ''bundle of universes'' type of diagram.
Figure 70-b shows another way to picture the action of the tangent functor on the logical transformation ''F''‹''u'', ''v''› = ‹((''u'')(''v'')), ((''u'', ''v''))›, roughly in the style of the ''bundle of universes'' type of diagram.