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Representation of n-abelian categories in abelian categories
- Source :
- Journal of Algebra 563 (2020) 352-375
- Publication Year :
- 2020
-
Abstract
- Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of absolutely pure group valued functors over $\mathcal{M}$, denote by $\mathcal{L}_2(\mathcal{M},\mathcal{G})$, is an abelian category and $\mathcal{M}$ is equivalent to a full subcategory of $\mathcal{L}_2(\mathcal{M},\mathcal{G})$ in such a way that $n$-kernels and $n$-cokernels are precisely exact sequences of $\mathcal{L}_2(\mathcal{M},\mathcal{G})$ with terms in $\mathcal{M}$. This gives a higher-dimensional version of the Freyd-Mitchell embedding theorem for $n$-abelian categories.
Details
- Database :
- arXiv
- Journal :
- Journal of Algebra 563 (2020) 352-375
- Publication Type :
- Report
- Accession number :
- edsarx.2001.01254
- Document Type :
- Working Paper