TL;DR
This paper investigates the foundational problem of characterizing all possible mappings on arbitrary nonvoid sets that can be identified solely through categorical means, highlighting its significance in foundational mathematics.
Contribution
It introduces a new problem in category theory concerning the identification of all mappings on sets using categorical methods, emphasizing its foundational importance.
Findings
Highlights the foundational relevance of the problem
Defines the scope of mappings identifiable via categories
Proposes a framework for analyzing such mappings
Abstract
The problem is posed to find out for arbitrary nonvoid sets which are all the mappings that can be defined and each separately identified through means of categories alone. As argued, this problem may have a certain foundational relevance.
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Taxonomy
TopicsAdvanced Algebra and Logic