Tom Leinster Abstract

There are many usages of the word "spectrum" in mathematics and the physical sciences.  With the possible exception of the way homotopy theorists use it, most of those usages are closely connected. I will focus on the most simple usage: the spectrum of a linear operator on a finite-dimensional vector space is its set of eigenvalues, with their algebraic multiplicities.  The appearance of these concepts on every undergraduate syllabus attests to their importance.  But is there a categorical explanation of where the spectrum comes from?  I will give one answer, and also say something about what the spectrum becomes when transplanted from the category of finite-dimensional vector spaces to other categories.

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