定向范畴论中的纤维化
Fibrations in Oriented Category Theory
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中文总结 AI 辅助
从定向范畴论角度研究高阶范畴纤维化，给出其等价特征，表明纤维化范畴构成定向范畴，研究其与定向拉回相互作用并构建相关纤维化版本及格罗滕迪克构造。
中文摘要 AI 辅助
我们从定向范畴论的角度研究高阶范畴的纤维化，该框架通过在格雷张量积中的系统富集来解释高阶范畴论中的松弛现象。我们给出了$(\infty,\infty)$-范畴和定向范畴纤维化的几个等价特征，并表明纤维化范畴自然地组织成定向范畴。我们研究了纤维化与定向拉回之间的相互作用，并构建了自由纤维化和通用纤维化的高阶范畴版本。后者产生了$(\infty,\infty)$-范畴和定向范畴纤维化的格罗滕迪克构造。
英文摘要
We study fibrations of higher categories from the perspective of oriented category theory, a framework which accounts for lax phenomena in higher category theory via systematic enrichment in the Gray tensor product. We give several equivalent characterizations of fibrations of $(\infty,\infty)$-categories and oriented categories, and show that categories of fibrations naturally organize to form oriented categories. We study the interaction between fibrations and oriented pullbacks and construct higher-categorical versions of free fibrations and universal fibrations. The latter give rise to Grothendieck constructions for fibrations of $(\infty,\infty)$-categories and oriented categories.
