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Oct 21, 2021 at 15:03 comment added Peter LeFanu Lumsdaine 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.
Oct 21, 2021 at 15:01 vote accept Jake Wetlock
Oct 21, 2021 at 15:01 history answered varkor CC BY-SA 4.0