Limits Colimits When to Use Use this skill when working on limits-colimits problems in category theory. Decision Tree 1. Identify Limit Type - Product: limit of discrete diagram - Equalizer: limit of parallel pair f, g: A - B - Pullback: limit of A - C <- B - Terminal object: limit of empty diagram - Lean 4: namespace 2. Verify Universal Property - Cone from L with projections pi i: L - D i - For any cone from X, unique morphism u: X - L - Triangles commute: pi i . u = cone i - Lean 4: gives the unique morphism 3. Colimit (Dual) - Coproduct: colimit of discrete diagram - Coequalizer: colimit…