On g-finiteness in the category of projective presentations

We provide new equivalent conditions for an algebra Λ to be g-finite, analogous to those established by L. Demonet, O. Iyama, and G. Jasso, but within the category of projective presentations K[-1,0](proj Λ). We show that an algebra has finitely many isomorphism classes of basic $2$-term silting objects if and only if all cotorsion pairs in K[-1,0](proj Λ) are complete. Furthermore, we establish that this criterion is also equivalent to all thick subcategories in K[-1,0](proj Λ) having enough injective and projective objects.