Jay Reiter, UW
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PDL C-401
To a stable infinity category \$C\$ equipped with a well-behaved homology functor to an abelian category \$A\$, Patchkoria--Pstrągowski associate a derived category which, in a precise sense, interpolates between cohomology objects in \$C\$ and descent spectral sequences in \$A\$ abutting to them. In this talk, we will begin by showing how this derived category arises naturally when trying to infinity-categorify injective resolutions and then take a close look at its construction which axiomatizes the deformation-theoretic ideas behind synthetic spectra.