The dark side of categorical Banach space theory

This paper could be considered the third in the series The Hitchhiker Guide to Categorical Banach Space Theory [24, 25]. We explore (quasi) Banach space formulations and applications for advanced categorical topics, such as relative homology (with either respect to size or relative to an operator ideal), Buchsbaum’s satellites (and homological derivation in quasi-Banach spaces), coherent functors and sheaves, Quillen’s adjunction theorem, Auslander’s formula, the Heart of the categories of Banach and quasi-Banach spaces, the vanishing of some Ext2 functors, Martsinkovsky-Russell stabilizations, nets of Banach spaces or 3-space problems.