MyWikiBiz, Author Your Legacy — Saturday May 04, 2024
Jump to navigationJump to search
4,661 bytes removed
, 15:18, 25 August 2007
Line 6,960: |
Line 6,960: |
| </font><br> | | </font><br> |
| | | |
− | <pre> | + | <br> |
− | o o
| + | <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> |
− | / \ / \
| |
− | / \ / O \
| |
− | / \ o /@\ o
| |
− | / \ / \ / \
| |
− | / \ / \ / \
| |
− | / O \ / O \ / O \
| |
− | o /@\ o o /@\ o /@\ o
| |
− | / \ / \ / \ \ / \ \ / \
| |
− | / \ / \ / \ / \ / \
| |
− | / \ / \ / O \ / O \ / O \
| |
− | / \ / \ o /@ o /@\ o /@ o
| |
− | / \ / \ / \ \ / \ / \ \ / \
| |
− | / \ / \ / \ / \ / \ / \
| |
− | / O \ / O \ / O \ / O \ / O \ / O \
| |
− | o /@ o /@ o o /@ o /@ o /@ o /@ o
| |
− | |\ / \ /| |\ / \ / / \ / / \ /|
| |
− | | \ / \ / | | \ / \ / \ / \ / |
| |
− | | \ / \ / | | \ / O \ / O \ / O \ / |
| |
− | | \ / \ / | | o /@ o @\ o /@ o |
| |
− | | \ / \ / | | |\ / \ / \ / \ / \ /| |
| |
− | | \ / \ / | | | \ / \ / \ / | |
| |
− | | u \ / O \ / v | | u | \ / O \ / O \ / | v |
| |
− | o-------o @\ o-------o o---+---o @\ o @\ o---+---o
| |
− | \ / | \ / \ / \ / \ / |
| |
− | \ / | \ / \ / |
| |
− | \ / | du \ / O \ / dv |
| |
− | \ / o-------o @\ o-------o
| |
− | \ / \ /
| |
− | \ / \ /
| |
− | \ / \ /
| |
− | o o
| |
− | U% $T$ $E$U%
| |
− | o------------------>o
| |
− | | |
| |
− | | |
| |
− | | |
| |
− | | |
| |
− | F | | $T$F
| |
− | | |
| |
− | | |
| |
− | | |
| |
− | v v
| |
− | o------------------>o
| |
− | X% $T$ $E$X%
| |
− | o o
| |
− | / \ / \
| |
− | / \ / \
| |
− | / \ / O \
| |
− | / \ o /@\ o
| |
− | / \ / \ / \
| |
− | / \ / \ / \
| |
− | / O \ / O \ / O \
| |
− | o /@\ o o /@\ o /@\ o
| |
− | / \ / \ / \ \ / \ / / \
| |
− | / \ / \ / \ / \ / \
| |
− | / \ / \ / O \ / O \ / O \
| |
− | / \ / \ o /@ o /@\ o @\ o
| |
− | / \ / \ / \ \ / \ / \ / \ / / \
| |
− | / \ / \ / \ / \ / \ / \
| |
− | / O \ / O \ / O \ / O \ / O \ / O \
| |
− | o /@ o @\ o o /@ o /@ o @\ o @\ o
| |
− | |\ / \ /| |\ / \ / \ / \ / \ / \ /|
| |
− | | \ / \ / | | \ / \ / \ / \ / |
| |
− | | \ / \ / | | \ / O \ / O \ / O \ / |
| |
− | | \ / \ / | | o /@ o @ o @\ o |
| |
− | | \ / \ / | | |\ / / \ / \ / \ \ /| |
| |
− | | \ / \ / | | | \ / \ / \ / | |
| |
− | | x \ / O \ / y | | x | \ / O \ / O \ / | y |
| |
− | o-------o @ o-------o o---+---o @ o @ o---+---o
| |
− | \ / | \ / / \ \ / |
| |
− | \ / | \ / \ / |
| |
− | \ / | dx \ / O \ / dy |
| |
− | \ / o-------o @ o-------o
| |
− | \ / \ /
| |
− | \ / \ /
| |
− | \ / \ /
| |
− | o o
| |
− | | |
− | 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. |