Topological Localization

Let ℰ , ℱ ℰ ℱ \mathcal{E},\mathcal{F} be a Presentable Infinity Categories, and L : ℰ → ℱ : 𝐿 → ℰ ℱ L:\mathcal{E}\to\mathcal{F} a Localization of Infinity Categories. We say that L 𝐿 L is a topological localization if the class of morphisms S ¯ ¯ 𝑆 \overline{S} of all morphisms f : X → Y : 𝑓 → 𝑋 𝑌 f:X\to Y in ℰ ℰ \mathcal{E} such that L ⁢ ( f ) 𝐿 𝑓 L(f) is an Equivalence is a Topological Class of Morphisms.