A Construction of Colimits in Monoidal Closed Categories
Alain Prout\'e
TL;DR
This paper proves that certain symmetric monoidal closed categories with specific completeness and cogenerating properties are necessarily cocomplete, expanding understanding of their structural capabilities.
Contribution
It establishes a new cocompleteness result for symmetric monoidal closed categories under particular conditions, linking monoidal structure with categorical completeness.
Findings
Symmetric monoidal closed categories with specified properties are cocomplete.
The result applies to small, well-powered categories with a small cogenerating family.
Provides a theoretical foundation for constructing colimits in such categories.
Abstract
We prove that a category which is symmetric (relaxed) monoidal closed, (small) complete, well-powered and has a small cogenerating family, is cocomplete.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Fuzzy and Soft Set Theory · Advanced Algebra and Logic