A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.

同伦类型理论中的反射子宇宙是拓扑或∞-范畴理论中局部化概念的内部版本。在同伦类型理论中，我们给出了反射子宇宙L上以下条件的新特征：（1）相关子宇宙${升}^{\prime }$的大号-分隔类型是一个模态; (2) L是一种情态；(3) L是 lex 模态；(4) L是共拓扑模态。在每种情况下，我们都给出了几个充要条件。我们表征涉及相关联的地图的各种家庭大号，如大号-étale映射中，大号-equivalences中，大号-local映射中，大号-连接的地图，该地图单元${\eta }_X$，以及它们的左和/或右正交补码。更一般地说，我们的主要定理概述了所有这些类如何相互关联。我们还给出了一些例子，表明我们在这些地图类之间描述的所有包含都可以是严格的。