Nonstandard model categories and homotopy theory

TL;DR

This paper explores how nonstandard methods can be applied to algebraic geometry by examining the behavior of homotopical constructions under enlargements in nonstandard model categories.

Contribution

It extends previous work on enlargements of categories to analyze the behavior of homotopical constructions in nonstandard model categories.

Findings

Homotopical constructions are compatible with enlargements.

Nonstandard methods can be effectively applied to algebraic geometry.

Extension of nonstandard techniques to homotopy theory.

Abstract

In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions behave under enlargements.