Session S27 - Categories and Topology

Wednesday, July 21, 19:00 ~ 19:30 UTC-3

The homotopy theory of simplicial Beck modules

Martin Frankland

University of Regina, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In his 1967 thesis, Beck proposed a notion of module over an object in a category C. This provided a natural notion of coefficient module for André-Quillen (co)homology of any algebraic structure, generalizing the original case of commutative rings. As one varies the object in C, the categories of Beck modules over different objects assemble into a fibered category over C, sometimes called the tangent category of C. Motivated by Quillen (co)homology, I will discuss the homotopy theory of simplicial Beck modules over simplicial objects, generalizing some work of Quillen on simplicial commutative rings.

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