论文标题
关于对称单体类别的全球同义理论
On the global homotopy theory of symmetric monoidal categories
论文作者
论文摘要
施威德（Schwede）引入了可行的类别，作为其全球代数$ k $ - 理论构建的投入。我们证明，他们相对于所谓的全球等效性的整个同质理论已经可以通过更平凡的对称单体类别来建模。 在另一个方向上，我们表明，由此产生的同义理论也等同于某种态度类别的某种简单类似物的同义理论，我们称之为典型的简单集。这些构成了我们在Arxiv中探索的多个“全球相干性单体”概念的桥梁，例如超交换性单体和全局$γ$ - 空间。
Parsummable categories were introduced by Schwede as input for his global algebraic $K$-theory construction. We prove that their whole homotopy theory with respect to the so-called global equivalences can already be modelled by the more mundane symmetric monoidal categories. In another direction, we show that the resulting homotopy theory is also equivalent to the homotopy theory of a certain simplicial analogue of parsummable categories, that we call parsummable simplicial sets. These form a bridge to several concepts of 'globally coherently commutative monoids' like ultra-commutative monoids and global $Γ$-spaces, that we explore in arXiv:2012.12676.
