Abstract
Let A be an exact category in which all infinite products exist and the functors of infinite product are exact. A complex C• over A is called Italic if it belongs to the minimal triangulated subcategory Acycl ctr (A) of the homotopy category Hot(A) containing all the total complexes of exact triples ′K• → K• → ″K• of complexes over A and closed under infinite products. Any contraacyclic complex is acyclic. It follows from the next lemma that any acyclic complex bounded from above is contraacyclic.
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© 2010 Springer Basel AG
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Positselski, L., Arkhipov, S., Rumynin, D. (2010). Derived Functor SemiExt. In: Homological Algebra of Semimodules and Semicontramodules. Monografie Matematyczne, vol 70. Springer, Basel. https://doi.org/10.1007/978-3-0346-0436-9_5
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DOI: https://doi.org/10.1007/978-3-0346-0436-9_5
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