functor categories
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2021 ◽  
pp. 1-24
Author(s):  
Martín Ortiz-Morales ◽  
Martha Lizbeth Shaid Sandoval-Miranda ◽  
Valente Santiago-Vargas
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Author(s):  
Martin Bies ◽  
Sebastian Posur

We provide explicit constructions for various ingredients of right exact monoidal structures on the category of finitely presented functors. As our main tool, we prove a multilinear version of the universal property of so-called Freyd categories, which in turn is used in the proof of correctness of our constructions. Furthermore, we compare our construction with the Day convolution of arbitrary additive functors. Day convolution always yields a closed monoidal structure on the category of all additive functors. In contrast, right exact monoidal structures for finitely presented functor categories are not necessarily closed. We provide a necessary criterion for being closed that relies on the underlying category having weak kernels and a so-called finitely presented prointernal hom structure. Our results are stated in a constructive way and thus serve as a unified approach for the implementation of tensor products in various contexts.







2020 ◽  
Vol 115 ◽  
pp. 100565 ◽  
Author(s):  
Jens Kosiol ◽  
Lars Fritsche ◽  
Andy Schürr ◽  
Gabriele Taentzer
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2020 ◽  
Vol 48 (7) ◽  
pp. 3133-3156
Author(s):  
Razieh Vahed
Keyword(s):  


2019 ◽  
Vol 62 (3) ◽  
pp. 564-583 ◽  
Author(s):  
YU LIU

AbstractIn this article, we study localizations of hearts of cotorsion pairs ($\mathcal{U}, \mathcal{V}$) where $\mathcal{U}$ is rigid on an extriangulated category $\mathcal{B}$ . The hearts of such cotorsion pairs are equivalent to the functor categories over the stable category of $\mathcal{U}$ ( $\bmod \underline{\mathcal{U}}$ ). Inspired by Marsh and Palu (Nagoya Math. J.225(2017), 64–99), we consider the mutation (in the sense of Iyama and Yoshino, Invent. Math.172(1) (2008), 117–168) of $\mathcal{U}$ that induces a cotorsion pair ( $\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$ ). Generally speaking, the hearts of ( $\mathcal{U}, \mathcal{V}$ ) and ( $\mathcal{U}^{\prime}, \mathcal{V}^{\prime}$ ) are not equivalent to each other, but we will give a generalized pseudo-Morita equivalence between certain localizations of their hearts.



2019 ◽  
Vol 223 (3) ◽  
pp. 1073-1096 ◽  
Author(s):  
Javad Asadollahi ◽  
Rasool Hafezi ◽  
Razieh Vahed


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