Preresolving status of LB inside (LB,D)

Investigate whether the full subcategory LB of regular LB-spaces is (uniformly) preresolving within the deflation-exact category (LB,D).

Background

Theorem MAIN-1 establishes derived equivalences using relative derived categories and standard resolutions. Whether LB is (uniformly) preresolving inside (LB,D) affects the applicability of general preresolving results and the extension of equivalences beyond bounded/right bounded cases.

References

If $LB\subseteq(LB,D)$ is (uniformly) preresolving is unknown.

— A homological approach to (Grothendieck's) completeness problem for regular LB-spaces  (2512.13161 - Wegner, 15 Dec 2025) in Remark following Theorem MAIN-1, Section 7 (Derived Categories)