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, 15:18, 25 August 2007
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| | </font><br> | | </font><br> |
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| + | <p>[[Image:Diff Log Dyn Sys -- Figure 70-a -- Tangent Functor Diagram.gif|center]]</p> |
| − | / \ / \
| + | <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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| − | / \ o /@\ o
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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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| − | o o
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| − | U% $T$ $E$U%
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| − | o------------------>o
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| − | F | | $T$F
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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))> | |
| − | </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. |
