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May 25, 2013 at 16:49 history edited Marc Hoyois CC BY-SA 3.0
added 900 characters in body
May 24, 2013 at 19:03 vote accept Alicia Garcia-Raboso
May 24, 2013 at 0:01 history edited Alicia Garcia-Raboso CC BY-SA 3.0
Corrected reference to HTT for the definition of n-localic infty-topos.
May 24, 2013 at 0:01 comment added Alicia Garcia-Raboso @Marc: thanks! This answers my question for the adjoint pair $f_! := \mathrm{Lan}_f \dashv f^\ast$ coming from a morphism of sites. There is another case I need in which $f$ is a so-called "cocontinuous" functor (pulls back coverings to coverings), in which case it is the pair $f^\ast \dashv f_\ast = \mathrm{Ran}_f$ that I want to derive. Am I right in thinking that the argument goes through, or is there some subtlety that I am missing?
May 23, 2013 at 19:05 history answered Marc Hoyois CC BY-SA 3.0