TL;DR
This paper develops a model structure for natural transformations of diagrams of simplicial presheaves, defining weak equivalences inspired by pro-equivalences between pro-objects, advancing the understanding of diagrammatic homotopy theory.
Contribution
It introduces a novel model structure for diagrams of simplicial presheaves with weak equivalences based on pro-equivalence concepts.
Findings
Defines a new model structure for diagrams of simplicial presheaves.
Establishes weak equivalences analogous to pro-equivalences.
Provides a framework for homotopy-theoretic analysis of diagrams.
Abstract
This paper presents a model structure for natural transformations of diagrams of simplicial presheaves of a fixed shape, in which the weak equivalences are defined by analogy with pro-equivalences between pro-objects.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Topics in Algebra