Remark 1.3.8. Despite the heavier notation, Axiom C.2 has exactly the same formal shape as the product part of the previous axiom: it introduces an \(\infty \)-category with structure, explains how compatible data on \(T\) determines a functor \(T \to X\), and says that such functors are determined up to natural isomorphism by that data. For a fully precise formulation of the final compatibility condition, we refer to Reference ? of [Cisinski et al. (2026)].
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