Codescent and Bicolimits of Pseudo-Algebras

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-04-09 DOI:10.1007/s10485-024-09765-0

Axel Osmond

引用次数: 0

Abstract

We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of codescent objects. After prerequisites on pseudomonads and their pseudo-algebras, we give a 2-dimensional Linton theorem reducing bicocompleteness of 2-categories of pseudo-algebras to existence of bicoequalizers of codescent objects. Finally we prove this condition to be fulfilled in the case of a bifinitary pseudomonad, ensuring bicocompleteness.

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伪代数的编码和双极限

我们以假单子为背景，对单子理论的共完备性结果进行分类。我们首先证明了一个一般性结果，即在任何二元范畴中，加权二元极限都可以从oplax二元极限和编码对象的二元均衡器构造出来。在假单胞及其伪代数的先决条件之后，我们给出了一个二维林顿定理，将伪代数的 2 维类的二重完备性简化为编码对象的二重均衡器的存在性。最后，我们证明这一条件在二元假单子的情况下得到满足，从而确保了二元完备性。

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.