higher category

高阶范畴

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Translation evidence: Literature usage

Meaning in context

A categorical structure with higher morphisms and coherent composition; the scoped (∞,1) model here is a simplicial set admitting fillers for every inner horn.

具有高阶态射和相容合成资料的范畴结构；本条限定的 (∞,1) 模型是每个内角都可填充的单纯集合。

Example

The nerve of an ordinary category and every Kan complex give (∞,1)(\infty,1)-category examples.

Usage and distinctions

Higher category is broader than (∞,1)-category; this entry fixes a model instead of claiming all higher theories share one definition.

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Definition sources

  1. Jacob Lurie — Higher Topos Theory (author IAS PDF)§1.1.2, Definition 1.1.2.4 and Examples 1.1.2.5–1.1.2.6; §6.1, Definition 6.1.0.4 · Checked 2026-10-14

Translation sources

  1. 徐斐（汕头大学）— 教师页面「研究介绍」末段：「高阶范畴理论」；仅支持中文名称的使用 · Checked 2026-10-14
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