论文标题
Abex与DEF之间的2类抗等于的单相似
A monoidal analogue of the 2-category anti-equivalence between ABEX and DEF
论文作者
论文摘要
我们证明，具有精确单体结构的2类骨骼小的阿贝尔类别与满足精确性标准的FP-HOM闭合可定义的可添加剂类别的2类抗等量。对于固定的有限访问类别$ \ MATHCAL {C} $带产品和满足适当假设的单体结构，我们在$ \ Mathcal {C} $的fp-hom锁定可定义的可定义子类别之间提供了两种物品， $ \ mathcal {c}^{\ Mathrm {fp}} \ hbox { - } \ Mathrm {mod} $和ziegler-type拓扑的封闭子集。对于带有添加剂，对称，刚性的单体结构的骨骼骨骼小的preaddive类别$ \ MATHCAL {a} $，我们表明，基本双重性会在$ \ \ mathrm {modrm {mod} \ hbox} \ hbox { - } \ mathable的$ \ mathrm {mathrm {mathrm {mathrm {mathrm {mathrm {mathrm { - } \ mathable的可定义子类别之间进行两次射击。 $ \ MATHCAL {A} \ HBOX { - } \ MATHRM {MOD} $。
We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to the 2-category of fp-hom-closed definable additive categories satisfying an exactness criterion. For a fixed finitely accessible category $\mathcal{C}$ with products and a monoidal structure satisfying the appropriate assumptions, we provide bijections between the fp-hom-closed definable subcategories of $\mathcal{C}$, the Serre tensor-ideals of $\mathcal{C}^{\mathrm{fp}}\hbox{-}\mathrm{mod}$ and the closed subsets of a Ziegler-type topology. For a skeletally small preadditive category $\mathcal{A}$ with an additive, symmetric, rigid monoidal structure we show that elementary duality induces a bijection between the fp-hom-closed definable subcategories of $\mathrm{Mod}\hbox{-}\mathcal{A}$ and the definable tensor-ideals of $\mathcal{A}\hbox{-}\mathrm{Mod}$.
