Enriched Pro-Categories and Shapes

Authors

DOI:

https://doi.org/10.37256/cm.3220221323

Keywords:

partially ordered set, category, functor, pro-category, pro-reflective subcategory, (abstract) shape, (abstract) coarse shape

Abstract

Given a category C and a directed partially ordered set J, a certain category proJ-C on inverse systems in C is constructed such that the ordinary pro-category pro-C is the most special case of a singleton J ≡ {1}. Further, the known pro*-category pro*-C becomes proN-C. Moreover, given a pro-reflective category pair (C, D), the J-shape category ShJ(C, D) and the corresponding J-shape functor SJ are constructed which, in mentioned special cases, become the well known ones. Among several important properties, the continuity theorem for a J-shape category is established. It implies the “J-shape theory” is a genuine one such that the shape and the coarse shape theory are its very special instances.

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Published

2022-04-24

How to Cite

1.
Uglešić N. Enriched Pro-Categories and Shapes. Contemporary Mathematics [Internet]. 2022 Apr. 24 [cited 2022 May 20];3(2):162-87. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1323