So, I believe that chain complexes of free R-modules are dualizable objects in a symmetric monoidal category $ch(R-mod)$. Thus, one can define a general trace for such objects using the evaluation and coevaluation maps associated with such objects. I have yet to go through the details of this but I was wondering if there was a simple definition for the trace of of endomorphisms of chain complexes of free R-modules, for instance the alternating sum of the traces of the individual maps in each degree? I'm not sure if this lines up with the more general categorical trace or if I have things confused. If anyone could point me to a source or provide a definition I would greatly appreciate it.
2026-04-02 11:33:29.1775129609
Trace for Endomoprhisms of Chain Complexes of Free R-Modules
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