In this paper we show how to compute left-Kan extensions of set-valued functors with the venerable chase algorithm from relational data base theory. The chase constructs an initial model of a particular finite-limit theory associated with each left-Kan extension. We also describe an algorithm based on this idea that achieves an order of magnitude improvement in our performance benchmarks compared to the next fastest known left-Kan extension algorithm, and explain how this algorithm specializes a particular kind of chase based on iterated push outs.

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