2-Limits and 2-Terminal Objects are too Different

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2022-09-08 DOI:10.1007/s10485-022-09691-z

tslil clingman, Lyne Moser

引用次数: 11

Abstract

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.

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2-极限和2-终端对象差别太大

在普通范畴论中，已知极限等价于锥的切片范畴中的终端对象。在本文中，我们证明了这个关于2-锥的2-极限和2-末端对象的定理的2-范畴类比在2-锥的2-范畴的各种选择中是假的。进一步证明，即使将2-锥弱化为伪自然变换或松弛自然变换，或考虑双型极限和双端对象，仍然不存在这种对应关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.