Twisted Arrow Construction for Segal Spaces
Chirantan Mukherjee, Nima Rasekh
TL;DR
This paper provides an explicit description of the twisted arrow construction for simplicial spaces, showing it preserves complete Segal space properties and that the projection forms a left fibration.
Contribution
It introduces an explicit construction for twisted arrows in simplicial spaces and proves key properties related to Segal spaces and fibrations.
Findings
Twisted arrow construction preserves complete Segal space properties.
The projection from the twisted arrow Segal space is a left fibration.
Explicit description aids in understanding simplicial space structures.
Abstract
We give an explicit description of the twisted arrow construction for simplicial spaces and demonstrate individually that it preserves the defining properties of a complete Segal space. Moreover, we show that for a Segal space, the natural projection from the twisted arrow Segal space is a left fibration.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology