Timeline for A question about the adjointness of two functors on presheaf categories induced by a functor on small categories
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2010 at 22:03 | comment | added | Peter LeFanu Lumsdaine | See several previous MO questions: mathoverflow.net/questions/33181/…, mathoverflow.net/questions/32791/…, mathoverflow.net/questions/23794/…… | |
| Dec 15, 2010 at 18:15 | comment | added | David Carchedi | You actually get THREE adjoint functors $f_!$, $f^*$, and $f_*$, with each adjoint to the adjacent. | |
| Dec 15, 2010 at 18:06 | comment | added | Todd Trimble | Yes, it is well-known that $f_\ast$ (under your notation; often one sees $f_!$) is left adjoint to $f^\ast$. It is saying that $f_\ast$ is the left Kan extension along $f^{op}$, and the requisite formula is a standard exercise in the yoga of the Yoneda lemma. A chatty discussion of it can be found at ncatlab.org/nlab/show/free+cocompletion | |
| Dec 15, 2010 at 17:59 | history | edited | Todd Trimble | CC BY-SA 2.5 |
fixed LaTeX
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| Dec 15, 2010 at 17:24 | comment | added | jackie boy | I appologize about the terrible formatting job. | |
| Dec 15, 2010 at 17:21 | history | asked | jackie boy | CC BY-SA 2.5 |