Computing left Kan extensions

We describe a new extension of the Todd–Coxeter algorithm adapted to computing left Kan extensions. The algorithm is a much simplified version of that introduced by Carmody and Walters (Category Theory, Proceedings of the International Conference Held in Como, Italy, 22–28 July 1990. Springer) in 1991. The simplification allows us to give a straightforward proof of its correctness and termination when the extension is finite.