Is there a name for an adjunction between two categories such that
i) the unit of the adjunction is a natural isomorphism,
ii) the counit of the adjunction is a natural isomorphism?
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$\begingroup$ Colocalization. $\endgroup$– Fernando MuroCommented Oct 21, 2021 at 14:53
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1 Answer
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An adjunction for which the unit is a natural isomorphism is called a coreflective adjunction. An adjunction for which the counit is a natural isomorphism is called a reflective adjunction.
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$\begingroup$ In particular, see “Proposition 3.1. (equivalent characterizations)” on the nlab page for reflective subcategory that varkor linked — item (2) of that is the counit being iso. $\endgroup$ Commented Oct 21, 2021 at 15:03