One can view closed symmetric monoidal categories as a linearization of category theory. It is a framework that allows one to talk about linear algebraic notions in categories without an obvious linear structure. Some examples include compactly generated pointed topological spaces, chain complexes, and spectra. In this talk, I'll introduce the definition of closed symmetric monoidal categories, and then discuss how the notions of duals and traces generalized to these examples.

Traces and duality in closed symmetric monoidal categories

Wed, Dec. 6 4:40pm (MATH 2…

Grad Student Seminar

Sylvia Maher (University of Colorado)

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In this talk I will discuss derived functors, which are universal homotopy-theoretic approximations to functors between categories equipped with a notion of homotopy theory. I will show how they generalize derived functors from homological algebra, and then talk about homotopy (co)limits, an important class of derived functors.