Abstract:
Each commutative algebra $A$ gives rise to a representation $\mathcal{L}_A$, which we call the Loday functor of $A$, of the category $\Omega$ of finite sets and surjective maps. In this paper we present two (infinite-dimensional) non-isomorphic algebras over $\mathbb{C}$ with isomorphic Loday functors, namely, the algebras of continuous functions on the Möbius strip and on the cylinder.
Key words and phrases:Loday functor, representation of category, category of finite sets and surjections, functor isomorphism.
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