通过严格投影提升PIE极限
Lifting PIE limits with strict projections
摘要：
我们给出了一个统一的直接证明的提升PIE限制的2-范畴的代数和（伪）态射，它精确地指定哪些投影的提升极限是严格的，并检测严格性。在文献中，这些限制被逐一取消，以便跟踪每种情况下的这些预测。我们在弱代数态射的更一般的上下文中工作，以便也包括松弛态射。在这种情况下，PIE极限也同时被提升，只要图中的某些特定箭头是伪态射。同样，这统一了以前已知的许多特定PIE限制的解除，这些限制也被单独处理。
英文摘要：
We give a unified direct proof of the lifting of PIE limits to the 2-category of algebras and (pseudo) morphisms, which specifies precisely which of the projections of the lifted limit are strict and detect strictness. In the literature, these limits were lifted one by one, so as to keep track of these projections in each case. We work in the more general context of weak algebra morphisms, so as to include lax morphisms as well. PIE limits are also all simultaneously lifted in this case, provided some specified arrows of the diagram are pseudo morphisms. Again, this unifies the previously known lifting of many particular PIE limits, which were also treated separately.
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。
