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Universal δ-functors and relative injective objects in the category of p-Banach spaces

  • Nazaret Trejo-Arroyo
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Abstract

Inspired by Grothendieck's foundational work, we establish that the sequence of functors (ExtnpBan(E,−))n ≥ 0 on the category of p-Banach spaces (0 < p < 1) forms a universal δ-functor. To this end, for any pair of p-Banach spaces E and X, we construct a p-Banach space 𝒩EX that renders each functor ExtnpBan(E,−) effaceable. Furthermore, we show that this space serves as a relative injective object for E and X, enabling the construction of relative injective presentations and proving that the functors ExtnpBan(E,−) are the right derived functors of ℒ(E,−). We will also examine the situation in the category of quasi-Banach spaces.

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Cite

BibTeXRIS
BibTeX
@misc{trejoarroyo2026universal,
  title = {{Universal $δ$-functors and relative injective objects in the category of $p$-Banach spaces}},
  author = {Nazaret Trejo-Arroyo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15226},
  eprint = {2609.15226},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15226},
}
RIS
TY  - UNPB
TI  - Universal δ-functors and relative injective objects in the category of p-Banach spaces
AU  - Nazaret Trejo-Arroyo
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.15226
UR  - https://arxiv.org/abs/2609.15226
AB  - Inspired by Grothendieck's foundational work, we establish that the sequence of functors (Ext^n_pBan(E,−))_n ≥ 0 on the category of p-Banach spaces (0 < p < 1) forms a universal δ-functor. To this end, for any pair of p-Banach spaces E and X, we construct a p-Banach space 𝒩_E^X that renders each functor Ext^n_pBan(E,−) effaceable. Furthermore, we show that this space serves as a relative injective object for E and X, enabling the construction of relative injective presentations and proving that the functors Ext^n_pBan(E,−) are the right derived functors of ℒ(E,−). We will also examine the situation in the category of quasi-Banach spaces.
ER  -