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arXiv · 2503.21434

Elgot Categories and Abacus Programs

Chad Nester
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Abstract

We introduce Elgot categories, a sort of distributive monoidal category with additional structure in which the partial recursive functions are representable. Moreover, we construct an initial Elgot category, the morphisms of which coincide with a lightly modified version of Lambek's abacus programs. The partial functions that are strongly representable in this initial Elgot category are precisely the partial recursive ones.

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Chad Nester. 2025-03-27. Elgot Categories and Abacus Programs. https://arxiv.org/abs/2503.21434

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