Abstract
Let Λ be an Artin algebra and [Formula: see text] be an object in [Formula: see text], the morphism category of Λ. We will describe the Auslander–Reiten translate of [Formula: see text], i.e. [Formula: see text], as an object in [Formula: see text]. It is shown that, even though there may not exist much information about the object [Formula: see text] in the general case, its kernel homomorphism, that is the inclusion Ker (f′) → M′, may be described in terms of some universal-type properties. When f is a monomorphism we will also study the homomorphism f′ and show that, under certain assumptions, f is minimal left almost split if and only if f′ is minimal right almost split.
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