论文标题
Frobenius的木化模块和DG-nerve
Frobenius templicial modules and the dg-nerve
论文作者
论文摘要
在ARXIV：2302.02484V2中提出了灯火柱对象，以为富集的准类别设置合适的简单框架。在Leinster之后，这些对象具有某些委员会的替代，以替代非 - 牙犯的外部图。在本文中，我们考虑了Frobenius templicial对象，从而将乘法重新引入图片。当对$ k $ k $ $ k $ k $的$ k $ modules富含超过$ k $ k $时，一方面，我们证明了（同源性）分级的DG类别与Frobenius Templicial模块之间的等效性。这种等效性产生了经典DG-neve的自然富集，将DG类别变成了模块中的准类别。假设有投影率条件，我们进一步证明，当它可以配备非缔合性Frobenius结构时，这些模块是模块中的准类别。
Templicial objects were put forth in arXiv:2302.02484v2 to set up a suitable simplicial framework for enriched quasi-categories. Following Leinster, these objects feature certain comultiplications as a replacement for outer face maps in the non-cartesian case. In the present paper, we consider Frobenius templicial objects, thus re-introducing multiplications into the picture. When enriching over $k$-modules for a commutative ring $k$, we prove an equivalence of categories between (homologically) positively graded dg-categories on the one hand and Frobenius templicial modules on the other hand. This equivalence yields a natural enrichment of the classical dg-nerve, turning dg-categories into quasi-categories in modules. Assuming a projectivity condition, we further prove that a templicial module is a quasi-category in modules precisely when it can be equipped with a nonassociative Frobenius structure.
