半立方体部落
A notion of semi-cubical tribe
AI总结：
本文提出了一种基于$J$-frames的$J$-部落构造方法，用于处理具有对称性和反向的半立方体图示的范畴。
摘要：
我们引入了一个一般性的$J$-部落概念，并在给定的部落$\mathcal{T}$中构造了$J$-frames的$J$-部落，其中$J$是一个合适的广义直接范畴。这一构造适用于具有对称性和反向的半立方体图示的半立方体范畴。
英文摘要：
The important notions our ideas revolve around are that of tribes, a class of categories aiming at modeling intensional type theory, and that of semi-cubical objects, for a category of cubes with symmetries and reversals. We introduce a general notion of $J$-tribes, tribes suitably enriched in presheaves over $J$, and $J$-frames in a tribe $\mathcal{T}$ as a category of $J$-shaped resolutions in $\mathcal{T}$, for a direct category $J$, and we construct the $J$-tribe of $J$-frames in $\mathcal{T}$. Similar notions of $R$-tribes and $R$-frames are introduced for $R$ a suitable generalized direct category, and corresponding properties are established thanks to a construction relating $R$ to a strictly direct category. In particular, our framework applies to semi-cubes, which is our main motivation, and yields an appropriate notion of a semi-cubical tribe.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
