Rigidification of quasi-categories

By Daniel Dugger, David I. Spivak. 2009

75 citations recorded by the source corpus.

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from Lurie's "Higher Topos Theory" regarding the rigidification process.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2bdf225342b73a5b8a084addadf684257e93fa9

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Mapping spaces in Quasi-categories (2009, methodology): “In [8] we gave another functor Cnec which accomplished the same task, and we proved that the mapping spaces C.”
Homotopy coherent adjunctions and the formal theory of monads (2013, unknown): “Its image under the action of the degeneracy operator σ0 : [5] → [4] is the 5-arrow”
∞-Categories for the Working Mathematician (2018, background): “9), which Dugger and Spivak refer to as a “flag of vertex data” [16].”