Corpus ID: 119165876

# Constructing the Unstable Motivic Homotopy Category Using $(\infty,1)$-Categories

@article{Brazelton2018ConstructingTU,
title={Constructing the Unstable Motivic Homotopy Category Using \$(\infty,1)\$-Categories},
author={T. Brazelton},
journal={arXiv: Algebraic Topology},
year={2018}
}
• T. Brazelton
• Published 28 September 2018
• Mathematics
• arXiv: Algebraic Topology
This is an expository paper providing an overview of the unstable motivic homotopy category using the theory of $(\infty,1)$-categories. In this paper, we examine two constructions in the literature and discuss their equivalence.

#### References

SHOWING 1-9 OF 9 REFERENCES
K-theory and the bridge from motives to noncommutative motives
Abstract In this work we present a new approach to the theory of noncommutative motives and use it to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work isExpand
Norms in motivic homotopy theory
• Mathematics
• Astérisque
• 2021
If $f : S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes : \mathcal{H}_{\bullet}(S')\to \mathcal{H}_{\bullet}(S)$, whereExpand
A1-homotopy theory of schemes
• Mathematics
• 1999
© Publications mathématiques de l’I.H.É.S., 1999, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand