Cubical models of $\infty$-presheaves and the Bousfield-Kan formula
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
TL;DR
This paper develops cubical models for $ $-presheaves and extends the Bousfield-Kan formula to a broad class of monoidal model categories, enhancing tools for homotopical algebra.
Contribution
It constructs covariant and cocartesian model structures on cubical set categories and generalizes the Bousfield-Kan formula to new settings.
Findings
Established covariant and cocartesian model structures on cubical categories.
Derived a generalized Bousfield-Kan formula applicable to various monoidal model categories.
Provided a framework for $ $-presheaves in cubical homotopy theory.
Abstract
We construct the covariant and the cocartesian model structures on the slice categories of cubical sets and marked cubical sets, respectively. As an application, we derive a version of the Bousfield-Kan formula for arbitrary cofibrantly generated monoidal model categories satisfying Muro's axiom.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Logic, programming, and type systems