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Section 4.27 (04VB): Localization in categories—The Stacks project
The identity morphism X \to X in S^{-1} \mathcal{C} is the equivalence class of the pair (\text{id} : X \to X, \text{id} : X \to X). Lemma 4.27.2. Let \mathcal{ ...
Reflective subcategory - Wikipedia
In mathematics, a full subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint.