We raise the question of saying what it means for a functor between abelian categories to preserve homology. We give a kind of answer and explore the reasons it is unsatisfactory in general (although fine for left or right exact functors).
Keywords: preservation of homology
2000 MSC: 18E10, 18A22
Theory and Applications of Categories,
 Vol. 16, 2006, 
No. 7, pp 132-143.
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