Weba subcategory to be contravariantly finite. The condition is given in terms of the left almost split morphism of the minimal approximation of an object not in the subcategory. … Web(b) every subcategory of mod A is covariantly finite; (c) every subcategory of mod A is contravariantly finite. Proof: (a) = (b), (c). It is easily seen [8, Prop. 4.21 that a …

CONTRAVARIANTLY FINITE SUBCATEGORIES

WebFeb 2, 2010 · Recently R. Takahashi proved a far reaching generalization: if X is a contravariantly finite resolving subcategory of mod-R and if any module X in X satisfies Ext n R (X, R) = 0, for n 0, then X ... WebLet ΛΛ\Lambdaroman_Λ be an artin algebra. We denote by mod ΛΛ\Lambdaroman_Λ the category of all finitely generated right ΛΛ\Lambdaroman_Λ-modules and by ind ΛΛ\Lambdaro gunstrumental gmod we are number one

Applications of contravariantly finite subcategories

WebJan 20, 2011 · Monomorphism categories, cotilting theory, and Gorenstein-projective modules. Pu Zhang. The monomorphism category is introduced, where is a full subcategory of the module category -mod of Artin algebra . The key result is a reciprocity of the monomorphism operator and the left perpendicular operator : for a cotilting -module , … WebFeb 1, 2024 · Let X be a contravariantly finite resolving subcategory of mod-Λ, the category of finitely generated right Λ-modules. We associate to X the subcategory SX (Λ) of the morphism category H (Λ ... Webtion 5) if and only if the resolving subcategory ‘T is contravariantly finite in mod /1 and every n-module has a finite resolution in ‘T; i.e., for each C in mod n there is an exact sequence 0 -+ X,, + . . . + X0 + C -+ 0 with the Xi in IT. In fact sending T to lT gives a one-one correspondence between boxercraft sherpa blanket