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. © 2003 Elsevier Science Ltd. All rights reserved.
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