Abstract
AbstractWe introduce the concept of homological Frobenius functors as the natural generalization of Frobenius functors in the setting of triangulated categories, and study their structure in the particular case of the derived categories of those of complexes and modules over a unital associative ring. Tilting complexes (modules) are examples of homological Frobenius complexes (modules). Homological Frobenius functors retain some of the nice properties of Frobenius ones as the ascent theorem for Gorenstein categories. It is shown that homological Frobenius ring homomorphisms are always Frobenius.
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