On linear exactness properties
| Autor: | Zurab Janelidze, Pierre-Alain Jacqmin |
|---|---|
| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Property (philosophy) Diagram (category theory) 010102 general mathematics Canonical morphism exactness property Epimorphism Characterization (mathematics) 01 natural sciences Matrix (mathematics) regular category approximate operation Mathematics::Category Theory 0103 physical sciences essentially algebraic category Regular category 010307 mathematical physics 0101 mathematics Algebraic number matrix property Mathematics linear Mal'tsev condition |
| Zdroj: | Journal of Algebra, Vol. 583, no.., p. 38-88 (2021) |
| Popis: | We study those exactness properties of a regular category C that can be expressed in the following form: for any diagram of a given ‘finite shape’ in C , a given canonical morphism between finite limits built from this diagram is a regular epimorphism. The main goal of the paper is to characterize essentially algebraic categories which satisfy this property via (essential versions of) linear Mal'tsev conditions, which are known to correspond to the so-called matrix properties. We then apply this characterization, along with our earlier work on preservation of exactness properties by pro-completions, to prove that these exactness properties can be reduced to matrix properties already in the general setting of regular categories. |
| Databáze: | OpenAIRE |
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