g-vector fans and picture categories are extended to 0-Auslander extriangulated categories, unifying tau-cluster morphism categories and earlier picture categories.
Iyama-Solberg correspondence for exact dg categories
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abstract
We generalize the notions of $d$-cluster tilting pair and $d$-Auslander exact dg category to $d$-precluster tilting triple and $d$-minimal Auslander--Gorenstein exact dg category. We give a bijection between equivalence classes of $d$-precluster tilting triples and equivalence classes of $d$-minimal Auslander--Gorenstein exact dg categories. Our bijection generalizes Iyama--Solberg correspondence for module categories.
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math.RT 1years
2026 1verdicts
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$g$-vector fans and picture categories for 0-Auslander extriangulated categories
g-vector fans and picture categories are extended to 0-Auslander extriangulated categories, unifying tau-cluster morphism categories and earlier picture categories.