2-Limits and 2-Terminal Objects are too Different
2-Limits and 2-Terminal Objects are too Different
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2 极限和 2 终端对象差异太大
DOI：
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发表时间：
2020
影响因子：
0.6
通讯作者：
L. Moser
中科院分区：
文献类型：
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作者：
T. Clingman;L. Moser
在普通范畴论中，已知极限相当于锥体切片范畴中的终端对象。在本文中，我们证明了该定理的 2-类别类似物在 2-锥体的切片 2-类别的各种选择中涉及 2-极限和 2-末端对象是错误的。此外，我们表明，即使将 2 锥体弱化为伪自然变换或松弛自然变换，或考虑双类型限制和双终端对象，仍然不存在这种对应关系。
In ordinary category theory, limits are known to be equivalent to terminal objects in the slice category of cones. In this paper, we prove that the 2-categorical analogues of this theorem relating 2-limits and 2-terminal objects in the various choices of slice 2-categories of 2-cones are false. Furthermore we show that, even when weakening the 2-cones to pseudo- or lax-natural transformations, or considering bi-type limits and bi-terminal objects, there is still no such correspondence.