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Abstract
A semilocalization of a category is a full reflective subcategory with the property that the reflector is semileftexact. There are many interesting examples of semilocalizations, as for instance any torsionfree subcategory of a semiabelian category. By specializing a result due to S. Mantovani, we first characterize the categories which are semilocalizations of exact Mal'tsev categories. We then prove a new characterization of protomodular categories in terms of binary relations, allowing us to obtain an abstract characterization of the semilocalizations of exact protomodular categories. This result is very useful to study the (hereditarily)torsionfree subcategories of semiabelian categories. Some examples are considered in detail in the categories of groups, crossed modules, commutative rings and topological groups. We finally explain how these results extend the corresponding ones obtained in the abelian context by W. Rump.
Original language  English 

Pages (fromto)  206232 
Number of pages  27 
Journal  Journal of Algebra 
Volume  454 
DOIs  
Publication status  Published  15 May 2016 
Keywords
 Semiabelian category
 Protomodular category
 Mal'tsev category
 Localization
 Semileftexact reflector
 Torsion theory
 Exact completion
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 1 Finished

Structural homotopy theory: a categorytheoretic study
Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M.
1/01/13 → 31/12/16
Project: Research