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opposite quasi-category (changes) in nLab

nLab opposite quasi-category (changes)

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Context

$(\infty,1)$ -Category theory

Contents

Idea
Definition
References

Idea

The general notion of opposite (∞,1)-category leads to a notion of opposite of a quasi-category , when (∞,1)-categories are incarnated as quasi-categories.

So the notion of opposite of a quasi-category generalizes the notion of opposite category from category theory.

Definition

Under the relation between quasi-categories and simplicial categories the opposite quasi-category is that corresponding to the obvious opposite SSet-enriched category. Concretely in terms of the simplicial set $S$ underlying the quasi-category, this amounts to reversing the order of the face and degeneracy maps:

S_n^{op} := S_n

(d_i : S_n^{op} \to S_{n-1}^{op}) := (d_{n-i} : S_n \to S_{n-1})

(s_i : S_n^{op} \to S_{n+1}^{op}) := (s_{n-i} : S_n \to S_{n+1}) \,.

References

Secton 1.2.1 in

Jacob Lurie, Higher Topos Theory

Last revised on September 4, 2024 at 10:01:27. See the history of this page for a list of all contributions to it.