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Sep 26, 2015 at 23:11 comment added Zhen Lin No, of course not. In the first place you have to apply [-, Set] to the diagram. After that you have to chase around a specific object.
Sep 26, 2015 at 19:11 comment added Tim Campion Hmm... but I don't think being an exact square, or even a comma square, is enough to make the legs into Kan extensions. This is really kind of puzzling! I think I may post it as an MO question...
Sep 25, 2015 at 19:37 history edited Tim Campion CC BY-SA 3.0
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Sep 25, 2015 at 19:30 history edited Tim Campion CC BY-SA 3.0
added 30 characters in body
Sep 25, 2015 at 15:23 comment added Zhen Lin Your diagram is a comma square, hence is an exact square in the sense of Guitart. This is part of an axiomatic theory of pointwise Kan extensions.
Sep 25, 2015 at 15:00 history answered Tim Campion CC BY-SA 3.0