Traces in monoidal categories
Stephan Stolz, Peter Teichner
TL;DR
This paper develops a generalized notion of trace in monoidal categories, unifying various existing trace concepts across different mathematical contexts.
Contribution
It introduces a new trace construction for endomorphisms in monoidal categories, extending previous trace notions to a broader categorical setting.
Findings
Constructs a trace and trace pairing for suitable endomorphisms in monoidal categories.
Generalizes the trace for dualizable objects and nuclear operators.
Provides a unified framework for trace concepts in different mathematical structures.
Abstract
The main result of this paper is the construction of a trace and a trace pairing for endomorphisms satisfying suitable conditions in a monoidal category. This construction is a common generalization of the trace for endomorphisms of dualizable ob jects in a balanced monoidal category and the trace of nuclear operators on a locally convex topological vector space with the approximation property.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra