Gorenstein cotorsion pairs induced by balanced pairs

@misc{golfis2026gorenstein,
  title = {{Gorenstein cotorsion pairs induced by balanced pairs}},
  author = {Konstantinos Golfis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31729},
  eprint = {2609.31729},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31729},
}

TY  - UNPB
TI  - Gorenstein cotorsion pairs induced by balanced pairs
AU  - Konstantinos Golfis
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.31729
UR  - https://arxiv.org/abs/2609.31729
AB  - Let (𝒳,𝒴) be an admissible balanced pair in a locally presentable abelian category 𝒜, and let ℰ be its induced exact structure. We study the class G(𝒳) of cycles of two-sided complexes with terms in 𝒳 that are both right and left 𝒳-acyclic. If 𝒳 is closed under direct summands and finite direct sums and is κ-Kaplansky for every sufficiently large regular cardinal κ, we prove that (G(𝒳),G(𝒳)^⊥ *) is a hereditary cotorsion pair relative to ℰ. For relative purity determined by finitely presented modules, we give two criteria for functorial completeness and show that relative periodic modules generate a functorially complete hereditary cotorsion pair. We also compute the relative Gorenstein objects, their right orthogonal, and explicit approximations for a family of exact structures over Dedekind domains.
ER  -