Properties of the derived functor I_6^*

Determine whether the functor I_6^* between the derived categories indicated in diagram (EXACT-FUN-DER) is full, faithful, and/or a triangle equivalence.

Background

The authors analyze inclusion functors between derived categories built from various exact and deflation-exact structures on LB and its subcategories. They prove non-fullness and non-faithfulness for several functors (I_1–I_5^), but leave I_6* unresolved. Clarifying the properties of I_6* would complete the picture of functorial relationships among the derived categories.

References

(iii) The properties of $I_6*$ are unknown.

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