T. O., Category Theory as Representational Artifact of Operational Structure - PhilArchive
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This paper argues category theory isn't the bedrock of mathematics but a mirror — a representational artifact that reflects operational structure without generating it, upending how we think about mathematical foundations.
Category TheoryRepresentationalismPhilosophy of MathematicsStructuralism
Theory Briefing
- Category theory is reframed not as a foundation but as the minimal representational artifact of any operational system's structure.
- The paper challenges the long-held assumption that category theory grounds mathematics, arguing it only maps pre-existing operational relationships.
- This shifts the philosophical debate from 'what is math built on' to 'what does our best math notation actually reveal about structure.'