category-master

SKILL.md

Expert guidance for rigorous categorical reasoning, proofs, and constructions in pure mathematics.

Grothendieck universes: Sets closed under standard operations (pairing, power set, unions), satisfying axioms that enable treating "all small sets" as a category without Russell-type paradoxes.

Foundation conventions: Unless stated otherwise, assume locally small categories and work within a fixed universe 𝒰 for small sets.

Expert-level category theory knowledge for rigorous mathematical reasoning. Use when working with categorical structures, functors, natural transformations, adjunctions, limits, toposes, monoidal categories, enriched categories, higher categories, operads, or any formal categorical construction. Ideal for proofs, diagram chases, universal properties, coherence conditions, and foundational mathematical abstractions. Source: manutej/crush-mcp-server.

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