4 problems

Weak cofiber-sequence presentation conjecture. The natural epimorphism

Waldhausen null-homotopy conjecture. The induced map

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…

Muro–Tonks presentation conjecture. These relations define a presentation of $K_1(\mathscr{W})$.