2023/09/25 by Huerta, Mindy Y., Mendoza, Octavio, Sáenz, Corina +1
#18G20 #18G25 (primary) 18G10 #18G35 (secondary) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2309.14576
In this work we introduce the notion of higher 𝔼-extension groups for an extriangulated category C and study the quotients Xn+1\vee/[X] and Xn+1\wedge/[X] when X is an (n+2)-rigid subcategory of C. We also prove (under mild conditions) that each one is equivalent to a suitable subcategory of the category of functors of the stable category of Xn\vee and the co-stable category of Xn\wedge, respectively. Moreover, it can be induced an exact structure through these equivalences and we analyze when such quotients are weakly idempotent complete, Krull-Schmidt or abelian. The above discussion is also considered in the particular case of an (n+2)-cluster tilting subcategory of C since in this case we know that Xn+1\vee=C=Xn+1\wedge. Finally, by considering the category of conflations of a exact category, we show that it is possible to get an abelian category from these quotients.