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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeMay 8th 2011
   • (edited May 8th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexNew entry [[zoranskoda:domain globalization of functors]] under development. The codomain globalization is more trivial. This are questions of extending the constructions related to Beck's comonadicity from categories to functors. Our interest with Gabi Bohm are mainly for covers by localizations with some equivariance/compatibility with respect to additional (co)monad, which are a matter of ongoing work. This compatibility is like, or some dual of the one in the definition of morphisms of [[Q-categories]] and also the compatibility of [[differential monad]]s and localization, studied by Lunts and Rosenberg. The latter is related to the classical fact that the assignment of ring of regular differential operators to a commutative ring $R\mapsto Diff(R)$ is compatible with exact localizations, in the sense that $S^{-1}R \mapsto S^{-1}Diff(R)$; and also to Beilinson's notion of [[D-affinity]].

   New entry domain globalization of functors (zoranskoda) under development. The codomain globalization is more trivial. This are questions of extending the constructions related to Beck’s comonadicity from categories to functors. Our interest with Gabi Bohm are mainly for covers by localizations with some equivariance/compatibility with respect to additional (co)monad, which are a matter of ongoing work. This compatibility is like, or some dual of the one in the definition of morphisms of Q-categories and also the compatibility of differential monads and localization, studied by Lunts and Rosenberg. The latter is related to the classical fact that the assignment of ring of regular differential operators to a commutative ring $R\mapsto Diff(R)$ is compatible with exact localizations, in the sense that $S^{-1}R \mapsto S^{-1}Diff(R)$; and also to Beilinson’s notion of D-affinity.