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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeJul 9th 2010
   • (edited Jul 9th 2010)
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexIn general, given an adjoint equivalence of categories F:C->D:G, there trivially exists an opposite adjunction H:D->C:P that is also an equivalence (since F is both left and right adjoint to G). Is the same true for Quillen equivalences? (This isn't so obvious to me.) If not, is there a name for such a special Quillen equivalence?

   In general, given an adjoint equivalence of categories F:C->D:G, there trivially exists an opposite adjunction H:D->C:P that is also an equivalence (since F is both left and right adjoint to G).

   Is the same true for Quillen equivalences? (This isn’t so obvious to me.)

   If not, is there a name for such a special Quillen equivalence?