Approximation properties of torsion classes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912046909489152 |
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| author | Cox, Sean Poveda, Alejandro Trlifaj, Jan |
| author_facet | Cox, Sean Poveda, Alejandro Trlifaj, Jan |
| contents | We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Maximum Deconstructibility} principle introduced in \cite{Cox_MaxDecon} requires large cardinals; it sits, implication-wise, between Vopěnka's Principle and the existence of an $ω_1$-strongly compact cardinal. (2) While deconstructibility of a class of modules always implies the precovering property by \cite{MR2822215}, the concepts are (consistently) non-equivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation properties of torsion classes Cox, Sean Poveda, Alejandro Trlifaj, Jan Logic Commutative Algebra Category Theory Rings and Algebras We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Maximum Deconstructibility} principle introduced in \cite{Cox_MaxDecon} requires large cardinals; it sits, implication-wise, between Vopěnka's Principle and the existence of an $ω_1$-strongly compact cardinal. (2) While deconstructibility of a class of modules always implies the precovering property by \cite{MR2822215}, the concepts are (consistently) non-equivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits. |
| title | Approximation properties of torsion classes |
| topic | Logic Commutative Algebra Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2406.02829 |