This blog post extends the initial functor semantics for equational reasoning from bare categories to categories with finite products, showing that the formalism requires only a minor modification—asking the initial functor to preserve products. The author introduces cartesian diagrams and demonstrates how limits can be taken within cartesian categories without substantive changes to the unary framework.
Background
This is part 3 of a series on diagrammatic equational reasoning, building on prior work connecting initial functors to e-graph-based term rewriting. The Topos Institute hosts research at the intersection of category theory and computer science.
- Source
- Lobsters
- Published
- Nov 9, 2026 at 02:23 AM
- Score
- 5.0 / 10