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

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