We study localizations of an extriangulated category B and localizations of hearts of twin cotorsion pairs on B. We also give a generalized nearly Morita equivalence between the certain localizations of hearts of cotorsion pairs.

We show that the p-dimensional noncommutative Yang–Mills model corresponding to a (p − 1)-brane allows solutions which correspond to lower branes. This may be interpreted as the Morita equivalence of noncommutative planes of various dimensions.

Two algebraic structures A and B are called categorically equivalent if there is a functor from the variety generated by A to the variety generated by B, carrying A to B, that is an equivalence of the varieties when viewed as categories. We characterize those algebras categorically equivalent to A when A is an algebra whose set of term operations is as large as possible subject to constraints p...

We explore two constructions in homotopy category with algebraic precursors in the theory of noncommutative rings and homological algebra, namely the Hochschild cohomology of ring spectra and Morita theory. The present paper provides an extension of the algebraic theory to include the case when M is not necessarily a progenerator. Our approach is complementary to recent work of Dwyer and Greenl...

We prove that for every group G and any two sets I, J , the Brandt semigroup algebras l(B(I,G)) and l(B(J,G)) are Morita equivalent with respect to the Morita theory of selfinduced Banach algebras introduced by Grønbæk. As applications, we show that if G is an amenable group, then for a wide class of Banach l(B(I,G))-bimodules E, and every n > 0, the bounded Hochschild cohomology groups H(l(B(I...