Stability properties characterising n-permutable categories
(2017) Theory and Applications of Categories — Vol. 32, n° 45, p. 1563-1587 (2017)
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- Authors
Jacqmin, Pierre-Alain 
- Abstract
- The purpose of this paper is two-fold. A first and more concrete aim is to characterise n-permutable categories through certain stability properties of regular epimorphisms. These characterisations allow us to recover the ternary terms and the (n+1)-ary terms describing n-permutable varieties of universal algebras. A second and more abstract aim is to explain two proof techniques, by using the above characterisation as an opportunity to provide explicit new examples of their use: - an embedding theorem for n-permutable categories which allows us to follow the varietal proof to show that an n-permutable category has certain properties; - the theory of unconditional exactness properties which allows us to remove the assumption of the existence of colimits, in particular when we use the approximate co-operations approach to show that a regular category is n-permutable
- Affiliations
University of Coimbra CMUC, Department of Mathematics Universidade do Algarve Departamento de Matemática
Citations
Jacqmin, P.-A., & Rodelo, D. (2017). Stability properties characterising n-permutable categories. Theory and Applications of Categories, 32(45), 1563-1587. https://hdl.handle.net/2078.5/268949 (Original work published 2017)