A short note on coherence and self-similarity
Let \({\mathcal C}\), \(\otimes\) be a strict monoidal category. An object \(N\) is weakly self-similar if \(N\otimes N\) is a retract of \(N\). The full subcategory of \({\mathcal C}\) generated by the object \(N\) and the tensor \(\otimes\) is denoted by \({\mathcal N}^{\otimes}\). The author proves that the Karoubi envelope of the monoid \(\text{End}(N)\) contains a subcategory generated by an object isomorphic to \(N\), and a non-strict tensor.
scientific article; zbMATH DE number 1839065