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The Commutant and Center of a Generalized Green Functor

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Abstract

After fixing a commutative ring with unit R, we present the definition of adequate category and consider the category of R-linear functors from an adequate category to the category of R-modules. We endow this category of functors with a monoidal structure and study monoids (generalized Green functors) over it. For one of these generalized Green functors, we define two new monoids, its commutant and its center, and study some of their properties and relations between them. This work generalizes the article [3].

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The author declares that the data supporting the findings of this study are available within the paper.

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Acknowledgements

I thank the anonymous referee for example 3.3.3. I thank S. Bouc, F. Marmolejo and N. Romero for all their ideas and suggestions.

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No funding was obtained for this study. The author has no relevant financial or non-financial interests to disclose.

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Correspondence to Sael Cruz Cabello.

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Communicated by Jiří Rosický.

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Cruz Cabello, S. The Commutant and Center of a Generalized Green Functor. Appl Categor Struct 32, 29 (2024). https://doi.org/10.1007/s10485-024-09785-w

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