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http://hdl.handle.net/1942/32598
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DC Field | Value | Language |
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dc.contributor.author | HENRARD, Ruben | - |
dc.contributor.author | VAN ROOSMALEN, Adam-Christiaan | - |
dc.date.accessioned | 2020-11-12T13:47:39Z | - |
dc.date.available | 2020-11-12T13:47:39Z | - |
dc.date.issued | 2020 | - |
dc.date.submitted | 2020-11-11T14:47:22Z | - |
dc.identifier.uri | http://hdl.handle.net/1942/32598 | - |
dc.description.abstract | One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category $\mathcal{E}$ can be (essentially uniquely) embedded into its exact hull ${\mathcal{E}}^{\textrm{ex}}$; this embedding induces a derived equivalence $\textbf{D}^b(\mathcal{E}) \to \textbf{D}^b({\mathcal{E}}^{\textrm{ex}})$. Whereas it is well known that Quillen's obscure axioms are redundant for exact categories, some one-sided exact categories are known to not satisfy the corresponding obscure axiom. In fact, we show that the failure of the obscure axiom is controlled by the embedding of $\mathcal{E}$ into its exact hull ${\mathcal{E}}^{\textrm{ex}}.$ In this paper, we introduce three versions of the obscure axiom (these versions coincide when the category is weakly idempotent complete) and establish equivalent homological properties, such as the snake lemma and the nine lemma. We show that a one-sided exact category admits a closure under each of these obscure axioms, each of which preserves the bounded derived category up to triangle equivalence. | - |
dc.language.iso | en | - |
dc.subject | Mathematics - Category Theory | - |
dc.subject | Mathematics - Category Theory | - |
dc.subject | Mathematics - K-Theory and Homology | - |
dc.subject | 18E05, 18G80 | - |
dc.subject.other | Mathematics - Category Theory | - |
dc.subject.other | Mathematics - K-Theory and Homology | - |
dc.subject.other | 18E05, 18G80 | - |
dc.title | On the obscure axiom for one-sided exact categories | - |
dc.type | Preprint | - |
local.format.pages | 27 | - |
local.bibliographicCitation.jcat | O | - |
local.type.refereed | Non-Refereed | - |
local.type.specified | Preprint | - |
dc.identifier.arxiv | 2010.11293 | - |
dc.identifier.url | http://arxiv.org/abs/2010.11293v1 | - |
local.provider.type | ArXiv | - |
local.uhasselt.uhpub | yes | - |
item.fulltext | With Fulltext | - |
item.contributor | HENRARD, Ruben | - |
item.contributor | VAN ROOSMALEN, Adam-Christiaan | - |
item.accessRights | Open Access | - |
item.fullcitation | HENRARD, Ruben & VAN ROOSMALEN, Adam-Christiaan (2020) On the obscure axiom for one-sided exact categories. | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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2010.11293v1.pdf | Non Peer-reviewed author version | 464.39 kB | Adobe PDF | View/Open |
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