Closedness properties of internal relations IV: Expressing additivity of a category via subtractivity
| dc.creator | Janelidze, Zurab | |
| dc.date | 2006-10-03 | |
| dc.date.accessioned | 2026-07-07T07:28:38Z | |
| dc.date.available | 2026-07-07T07:28:38Z | |
| dc.description | The notion of a subtractive category, recently introduced by the author, is a ``categorical version'' of the notion of a (pointed) subtractive variety of universal algebras, due to A. Ursini. We show that a subtractive variety $\C$, whose theory contains a unique constant, is abelian (i.e. $\C$ is the variety of modules over a fixed ring), if and only if the dual category $\C^\mathrm{op}$ of $\C$, is subtractive. More generally, we show that $\C$ is additive if and only if both $\C$ and $\C^\mathrm{op}$ are subtractive, where $\C$ is an arbitrary finitely complete pointed category, with binary sums, and such that each morphism $f$ in $\C$ can be presented as a composite $f=me$, where $m$ is a monomorphism and $e$ is an epimorphism. | |
| dc.description | to be published in "Journal of Homotopy and Related Structures" | |
| dc.identifier | https://arxiv.org/abs/math/0610110 | |
| dc.identifier | http://arxiv.org/abs/math/0610110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117808 | |
| dc.subject | Category Theory | |
| dc.title | Closedness properties of internal relations IV: Expressing additivity of a category via subtractivity | |
| dc.type | text |