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A fibrational mate correspondence for $infty$-categories

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 نشر من قبل Rune Haugseng
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Rune Haugseng




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We study lax families of adjoints from a fibrational viewpoint, obtaining a version of the mate correspondence for (op)lax natural transformations of functors from an $infty$-category to the $(infty,2)$-category of $infty$-categories. We apply this to show that the left adjoint of a lax symmetric monoidal functor is oplax symmetric monoidal and that the internal Hom in a closed symmetric monoidal $infty$-category is lax symmetric monoidal in both variables. We also consider units and counits of such families of adjoints, and use them to derive the full (twisted) naturality of passing to the dual.



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