6 problems

Let $\mathcal{C}$ be a Waldhausen category, and let $\operatorname{End}(\mathcal{C})$ be its category of endomorphisms. Let $\widetilde{K}(\operatorname{End}(\mathcal{C}))$ be the…

Let $A$ be a ring, let $\widetilde{K}(\operatorname{End}(A))$ be the reduced algebraic $K$-theory spectrum of its category of endomorphisms, and let…

Let $\operatorname{Set}^{\mathrm{fin}}_{\cong}$ be the category of finite sets and bijections, let $\widetilde{K}(\operatorname{Set}^{\mathrm{fin}}_{\cong})$ denote its reduced alg…

Let $A$ be a ring, let $\operatorname{End}(A)$ be its category of endomorphisms, and let $V^{\geq j}\widetilde{K}(\operatorname{End}(A))$ be the induced Verschiebung filtration. Wr…

Let $A$ be the ring under consideration, and let $\widetilde{K}(\operatorname{End}(A))$ denote the reduced algebraic $K$-theory spectrum of its category of endomorphisms. Let…

Let $R$ be a ring, and let the sphere spectrum serve as the ground ring in place of the integers. Topological Hochschild and cyclic homology are the corresponding homological theor…