Rota-Baxter Categories

We introduce Rota-Baxter categories and construct examples of such structures.

💡 Research Summary

The paper introduces a categorical generalization of the classical Rota‑Baxter operator, termed a “Rota‑Baxter category.” After a brief motivation that highlights the importance of Rota‑Baxter algebras in combinatorics, quantum field theory, and algebraic topology, the authors set up the necessary background on monoidal categories, endofunctors, and natural transformations. They then define a Rota‑Baxter category as a triple ((\mathcal{C},R,\beta)) where (\mathcal{C}) is a monoidal category, (R:\mathcal{C}\to\mathcal{C}) is an endofunctor, and (\beta:R\circ R\Rightarrow R) is a natural transformation satisfying the categorical analogue of the Rota‑Baxter equation
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