Category Theory - GoKawiil

Topos Institute blog post outlines categorical framework for e-graph equational reasoning

A new post cross-published on the Topos Institute blog examines e-graphs, the congruence-maintaining data structures used in tools like egg and egglog for equational reasoning and computer algebra. The author reviews recent proposals by two research groups to give e-graphs categorical semantics via 'e-hypergraphs,' and introduces plans for an alternative concept called an 'e-diagram' built around the notion of an initial functor. The piece is framed as the first in a series exploring how diagrams can be used to prove equations.

epatters.org · 2026-11-08

Category theorist extends Yoneda Lemma to double categories without presheaves

A category theory writeup describes how to construct a Yoneda-style embedding within double categories, a setting where presheaves cannot be directly expressed because objects are treated as abstract 0-cells rather than sets. The author sketches how to define a presheaf object and a Yoneda vertical arrow using universal constructions like horizontal arrows and left Kan extensions instead of direct references to sets or presheaves. A follow-up post is promised that will implement these ideas as working code in Haskell.

bartoszmilewski.com · 2026-09-14