On the Unicity of the Homotopy Theory of Higher Categories
نویسنده
چکیده
We propose four axioms that a quasicategory should satisfy to be considered a reasonable homotopy theory of (∞, n)-categories. This axiomatization requires that a homotopy theory of (∞, n)-categories, when equipped with a small amount of extra structure, satisfies a simple, yet surprising, universal property. We further prove that the space of such quasicategories is homotopy equivalent to (RP∞)n. In particular, any two such quasicategories are equivalent. This generalizes a theorem of Toën when n = 1, and it verifies two conjectures of Simpson. We also provide a large class of examples of models satisfying our axioms, including those of Joyal, Kan, Lurie, Rezk, and Simpson.
منابع مشابه
Research Narrative
Introduction – Categorifying Parshin’s conjecture 1 1. Higher categories and unicity 2 1.1. Iterated complete Segal spaces 3 1.2. Relative categories and higher relative categories 3 1.3. The Unicity Theorem 3 2. Algebraic K-theory 3 2.1. The new fundamental theorems of K-theory 4 2.2. TheTheorem of the Heart 4 2.3. New localization sequences 4 2.4. Deligne Conjecture for K-theory 4 2.5. A high...
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