论文标题
比较定向同喻的非阴谋和统一设置
Comparing the non-unital and unital settings for directed homotopy
论文作者
论文摘要
本说明探讨了流的Q模型结构与拓扑丰富的小型类别的ILIAS模型结构之间的联系。两者都有较弱的等效性，可诱导基本（半）类别的等效性。 ILIAS模型结构不能沿左伴随添加身份图左转。在具有联合启动的流量上的最小模型结构的最小模型结构的左凸iLIAS模型结构的左启动的同质类别等于$ 3 $ - 元素完全有序的集合。流的Q模型结构可以右转到拓扑丰富的小型类别的Q模型结构，这是最小的，因此弱等价会导致基本类别的等价。拓扑丰富的小型类别的身份函数既不是左quillen的伴随，也不是Q-Model结构和ILIAS模型结构之间的右Quillen伴随。
This note explores the link between the q-model structure of flows and the Ilias model structure of topologically enriched small categories. Both have weak equivalences which induce equivalences of fundamental (semi)categories. The Ilias model structure cannot be left-lifted along the left adjoint adding identity maps. The minimal model structure on flows having as cofibrations the left-lifting of the cofibrations of the Ilias model structure has a homotopy category equal to the $3$-element totally ordered set. The q-model structure of flows can be right-lifted to a q-model structure of topologically enriched small categories which is minimal and such that the weak equivalences induce equivalences of fundamental categories. The identity functor of topologically enriched small categories is neither a left Quillen adjoint nor a right Quillen adjoint between the q-model structure and the Ilias model structure.
