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

TL;DR

This paper reviews how the unstable motivic homotopy category can be constructed using $( abla,1)$-categories, comparing two existing methods and discussing their equivalence.

Contribution

It provides an expository overview and comparison of two constructions of the unstable motivic homotopy category within the framework of $( abla,1)$-categories.

Findings

Demonstrates the equivalence of two different constructions

Clarifies the role of $( abla,1)$-categories in motivic homotopy theory

Provides insights into the structure of the unstable motivic homotopy category

Abstract

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.