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We describe a generic construction of non-wellfounded syntax involvingvariable binding and its monadic substitution operation. Our construction ofthe syntax and its substitution takes place in category theory, notably byusing monoidal categories and strong functors between them. A language isspecified by a multi-sorted binding signature, say {\Sigma}. First, we providesufficient criteria for {\Sigma} to generate a language of possibly infiniteterms, through {\omega}-continuity. Second, we construct a monadic substitutionoperation for the language generated by {\Sigma}. A cornerstone in thisconstruction is a mild generalization of the notion of heterogeneoussubstitution systems developed by Matthes and Uustalu; such a systemencapsulates the necessary corecursion scheme for implementing substitution.The results are formalized in the Coq proof assistant, through the UniMathlibrary of univalent mathematics.

Substitution for Non-Wellfounded Syntax with Binders through Monoidal Categories