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On endomorphisms of topological Hochschild homology
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abstract
We compute endomorphisms of topological Hochschild homology ($\mathrm{THH}$) as a functor on stable $\infty$-categories, as well as variants thereof: we also compute endomorphisms of the $k$-linear Hochschild homology functor $\mathrm{HH}_k$ over some base $k$; and endomorphisms of $\mathrm{THH}$ as a functor on stably symmetric monoidal $\infty$-categories.
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$\mathrm{Mot}^{\mathrm{loc}}$ is not compactly generated
For any connective E2-ring R with R_Q ≠ 0, the ∞-category of R-linear localizing motives is not compactly generated.
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