Timeline for When is the $(F_!,F^*)$ counit a natural isomorphism?
Current License: CC BY-SA 2.5
4 events
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| Jun 29, 2010 at 20:51 | comment | added | David Spivak | Hi David, the intended application is to "categorical information theory." One can consider a small category $C$ as a "database schema" and a $C$-set as data of that specification. A morphism of schemas is just a functor $f\colon C\to D$ between categories. It induces the two aforementioned adjunctions, each of which has real-world meaning. A user of a database $(D, x\colon D\to Set)$ might have access to a small part $C$ and he may update $f^\star x$. These updates in $C$ can be transported to $D$ using $f_!$ and $f_\star$. I'm looking at the effects of various kinds of updates. | |
| Jun 29, 2010 at 19:39 | comment | added | David Carchedi | No problem :-). I'm curious, what is your intended application? Perhaps there's more that can be said. | |
| Jun 29, 2010 at 19:04 | comment | added | David Spivak | Thanks David. This is a really helpful answer. In particular, it answers another question I was preparing to think about, namely "when is the unit of the (F^*,F_*) adjunction an isomorphism?" You point out that the answers to this new question and the question above agree. | |
| Jun 29, 2010 at 17:59 | history | answered | David Carchedi | CC BY-SA 2.5 |