most recent 30 from http://mathoverflow.net 2013-06-19T06:17:41Z http://mathoverflow.net/feeds/question/67389 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67389/on-locally-reflective-subcategories David Carchedi 2011-06-09T22:38:57Z 2011-06-09T22:51:53Z

<p>I am interested in the following situation:</p> <p>Suppose that $i:C \to D$ is a functor, $C$ does not necessarily have a terminal object, and for each object $c$ of $C,$ the induced functor</p> <p>$$C/c \to D/i(c)$$ is full and faithful and has a left-adjoint. Probably, one should say that $C$ is locally-reflective in $D$.</p> <p>Has this situation been studied? It is not necessarily important that the induced functors are full and faithful, but it is in my example (but $i$ itself is not).</p> <p>In such a situation, what can we say about induced functors between the presheaf categories of $C$ and $D$?</p> <p>Of course, I can work this all out for myself, but, if this has already been studied, I would like to know. Thanks!</p>