AI 中文总结
研究幺半模型范畴的富集变化，将经典范畴论定理扩展到该范畴，在特定假设下改进先前结果。以链复形范畴为例，其两种幺半结构产生幺半模型范畴，还借此重现增广dg - 范畴的平方零扩张伴随。
AI 中文摘要
范畴论的一个经典定理表明，给定具有宽松幺半右伴随的幺半范畴之间的一个伴随，在富集范畴的范畴之间存在一个诱导伴随。我们将此结果扩展到幺半模型范畴（在一些模型范畴假设下），改进了先前要求导出左伴随是强幺半的定理。作为应用，我们考虑在不同算子广群上的链复形范畴，配备两种不同的幺半结构：标准张量积和笛卡尔积。我们表明这两种积都产生幺半模型范畴，并使用我们的定理重现增广dg - 范畴的平方零扩张伴随。
英文摘要
A classical theorem of category theory says that given an adjunction between monoidal categories with lax monoidal right adjoint, there is an induced adjunction between categories of enriched categories. We extend this result to monoidal model categories (with some model categorical assumptions), improving on previous theorems which required the derived left adjoint to be strong monoidal. As an application, we consider the category of chain complexes over a varying groupoid of operators, equipped with two different monoidal structures: the standard tensor product, and the cartesian product. We show that both of these products yield monoidal model categories, and use our theorems to reproduce the square-zero extensions adjunction for augmented dg-categories.
Comments35 pages. Expands on some technical material originally in arXiv:2510.04254. Comments welcome!
