category-master

Universal properties are verified through diagram chasing and componentwise reasoning. category-master provides structured templates for establishing that a morphism satisfies the universal property by checking commutativity conditions and uniqueness of factorizations across all objects in relevant categories.

Prove functor and natural transformation theorems by decomposing into naturality checks and coherence conditions. category-master guides step-by-step verification of naturality squares and triangle identities, ensuring proofs hold in abstract settings like higher categories and toposes.

Yes. category-master applies adjunction proofs through explicit verification of unit and counit triangle identities, and extends reasoning to operads, monoidal categories, and higher categories with size considerations and Grothendieck universe constraints.

Structure proofs using formal verification templates that enforce coherence conditions and diagram-chasing discipline. category-master documents each proof step with explicit reasoning patterns, componentwise checks, and size constraints suitable for PhD-level mathematical research.

Use universal property verification, diagram chasing, and explicit documentation of all assumptions including size hierarchies. category-master enforces naturality checks and triangle identities as standard verification steps to catch gaps in abstract categorical reasoning.