One of the main motivations for Homotopy Type Theory (HoTT) is the way it treats of identity and the rich ∞-groupoid structure of types and identifications to which this gives rise. This paper investigates the conceptual and philosophical status of identity in HoTT. We examine the formal and technical features of identity types in the theory, and how these relate to other features of the theory such as its intensionality, constructive logic, and the interpretation of types as propositions and concepts. We explore the possibility that identity types might be better understood as encoding the indiscernibility of two tokens. We argue that identity types are a primitive component of HoTT.

中文翻译：

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同伦类型理论中的同一性：第二部分，HoTT 中同一性的概念和哲学地位

同伦类型理论 (HoTT) 的主要动机之一是它处理身份的方式以及由此产生的丰富的 ∞-groupoid 类型和身份结构。本文研究了 HoTT 中身份的概念和哲学地位。我们研究了该理论中身份类型的形式和技术特征，以及这些特征与该理论的其他特征（例如其内涵、构造逻辑以及将类型解释为命题和概念）之间的关系。我们探索身份类型可能被更好地理解为编码两个令牌的不可分辨性的可能性。我们认为身份类型是 HoTT 的原始组件。