synthetic-adjunctions

What problem does it solve?

This Skill encodes and generates adjunction data from directed type theory, enabling automated construction of universal structures such as limits, colimits, Kan extensions, and monads.

Core Features & Use Cases

• Unit/counit generation: produce η and ε for adjunctions, with coherence via triangle identities.
• Universal-property synthesis: derive left/right adjoints and their universal characterizations automatically.
• Practical templates: furnish ready-to-use adjunctions for common constructions (free-forgetful, Kan extensions, etc.).
• Use Case: given a functor F: A → B, synthesize its adjoint G and verify triangle identities.

Quick Start

Just run: just adjunction-generate --free-on Monoid or just adjunction-unit-counit L R