In their paper "Generators and bases for algebras over a monad" (https://arxiv.org/pdf/2010.10223.pdf) Zetzsche, Silva and Sammartino introduce the Symmetric algebra monad. It is an endofunctor in the category of vector spaces over a given field $k$ that sends a vector space to its symmetric algebra and a linear map to the unique algebra homomorphism obtained by the universal property of the symmetric algebra. They claim that this endofunctor is a monad where "multiplication flattens tensors over tensors in the usual way." What is meant by this quote? How is the multiplication of the symmetric algebra monad defined?
2026-03-26 08:03:31.1774512211
On the multiplication of the symmetric algebra monad
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