TL;DR
This paper explores the concepts of linearization and categorification across various mathematical and computational examples, highlighting their roles in adding structure and understanding complex invariants.
Contribution
It provides a unified discussion of linearization and categorification with illustrative examples, emphasizing their significance in mathematical theory and applications.
Findings
Linearization simplifies complex structures like PageRank and quantum invariants.
Categorification adds depth by enriching structures, as seen in representation theory and quantum invariants.
The paper clarifies the relationship between linearization and categorification in mathematical contexts.
Abstract
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of structure, in the context of the last two examples.
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