2024/09/05 by Miranda, M. Lizbeth Shaid Sandoval, Vargas, Valente Santiago, Páez, Edgar O. Velasco
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2409.03910
This paper focuses on defining an analog of differential-graded triangular matrix algebra in the context of differential-graded categories. Given two dg-categories U and T and M ∈ DgMod(U ⊗ Top), we construct the differential graded triangular matrix category Λ:= ( \beginsmallmatrix T & 0 M & U \endsmallmatrix ). Our main result is that there is an equivalence of dg-categories between the dg-comma category (DgMod(T),GDgMod(U)) and the category DgMod( ( \beginsmallmatrix T & 0 M & U \endsmallmatrix )). This result is an extension of a well-known result for Artin algebras (see, for example, [2,III.2].