Revista de la
Unión Matemática Argentina
Clones from comonoids
Ulrich Krähmer and Myriam Mahaman

Volume 68, no. 2 (2025), pp. 369–394    

Published online (final version): July 16, 2025

https://doi.org/10.33044/revuma.3951

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Abstract

We revisit the fact that the cocommutative comonoids in a symmetric monoidal category form the best possible approximation by a cartesian category, now considering the case where the original category is only braided monoidal. This leads to the question of when the endomorphism operad of a comonoid is a clone (a Lawvere theory). By giving an explicit example, we prove that this does not imply that the comonoid is cocommutative.

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