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Stream: theory: category theory

Topic: closed Grothendieck construction

Christian Williams (Oct 21 2020 at 05:54):

Joe Moeller and Christina Vasilakopoulou proved in "Monoidal Grothendieck Construction" https://arxiv.org/abs/1809.00727 that monoidal indexed categories are equivalent to monoidal fibrations. Does anyone know whether the analogous statement for closed structure has been proved? It appears to be folklore, though it is often assumed in categorical logic and elsewhere.