Morphisms determined by objects in triangulated categories
Henning Krause
TL;DR
This paper explores how morphisms determined by objects can be effectively constructed and classified within triangulated categories with Serre duality, offering new insights into their structure and applications.
Contribution
It demonstrates the effectiveness of morphisms determined by objects in triangulated categories with Serre duality and reformulates Freyd's generating hypothesis using this concept.
Findings
Effective classification of morphisms in triangulated categories
Application to reformulating Freyd's generating hypothesis
Enhanced understanding of morphism structures in categories with Serre duality
Abstract
The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of this concept arises from a reformulation of Freyd's generating hypothesis.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra