
TL;DR
This paper introduces the category of regular simplicial sets, highlighting its stability properties and cartesian closedness, contrasting it with finite simplicial sets.
Contribution
It defines the subcategory of regular simplicial sets and proves its stability and cartesian closedness, which are not present in finite simplicial sets.
Findings
The subcategory of regular simplicial sets is stable under limits and unions.
The category of finite regular simplicial sets is cartesian closed.
Finite simplicial sets are not cartesian closed.
Abstract
We define an interesting sub-category of the category of simplicial sets, , whose objects are called regular. Both it and the subcategory of finite regular simplicial sets have good stability properties under limits and union. The category is cartesian closed, in contrast to the category of finite simplicial sets which is not cartesian closed.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Peroxisome Proliferator-Activated Receptors · Metal-Catalyzed Oxygenation Mechanisms
