Various notions of (co)simplicial (pre)sheaves
Timothy Hosgood
TL;DR
This survey explores different interpretations of (co)simplicial (pre)sheaves, analyzing their relationships and providing examples of applications for the most general notions.
Contribution
It clarifies the various notions of (co)simplicial (pre)sheaves and their interrelations, offering insights into their applications.
Findings
Different interpretations of (co)simplicial (pre)sheaves are related and comparable.
The most general notions have practical applications demonstrated through examples.
The survey provides a unified perspective on these concepts.
Abstract
The phrase "(co)simplicial (pre)sheaf" can be reasonably interpreted in multiple ways. In this survey we study how the various notions familiar to the author relate to one another. We end by giving some example applications of the most general of these notions.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic structures and combinatorial models