Homological Epimorphisms and Hochschild-Mitchell Cohomology

2023/03/06 by Santiago-Vargas, V., Velasco-Páez, E. O. · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2303.03554

Abstract

In this work, we study the Hochschild-Mitchell Cohomology of triangular matrix categories. Given a triangular matrix category Λ=[ \beginsmallmatrix T & 0 M & U \endsmallmatrix], we investigate the relationship of the Hochschild-Mitchell cohomologies Hⁱ(Λ) and Hⁱ(U) of Λ and U respectively; and we show that they can be connected by a long exact sequence. This result extend the well-known result of Michelana-Platzeck given in [S. Michelena, M. I. Platzeck. \itHochschild cohomology of triangular matrix algebras. J. Algebra 233, (2000) 502-525].

Cited by

• Homological epimorphisms in functor categories and singularity categories

Related

• Hochschild cohomology of triangular matrix algebras
• Hochschild-Mitchell cohomology and Galois extensions
• Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions
• Cibils'spectral sequence for the cohomology of triangular algebras
• Applications of the change-of-rings spectral sequence to the computation of Hochschild cohomology