Abstract We construct a non-affine analogue of the singularity category Gorenstein local ring. With this, Buchweitz’s classic equivalence three triangulated categories over ring has been generalized to schemes, project started by Murfet and Salarian more than ten years ago. Our construction originates in framework we develop for exact categories. As an application this non-commutative setting, ...

Analysis of the current state education, its functions in conditions globalization processes and transformations taking place 21st century at international level general within states themselves give grounds for asserting a new understanding essence education as an integral category terms formation creative personality, life activities, development society state, further improvement interstate ...

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.

People exhibit the ability to imagine new category instances and new categories, with examples ranging from everyday activities like cooking to scientific discovery. This ability, which we call category generation, is not addressed by standard models of category learning, which focus on classifying instances rather than generating them. We develop a probabilistic account of category generation ...

This article presents a development of Category Theory in Isabelle. A Category is defined using records and locales in Isabelle/HOL. Functors and Natural Transformations are also defined. The main result that has been formalized is that the Yoneda functor is a full and faithful embedding. We also formalize the completeness of many sorted monadic equational logic. Extensive use is made of the HO...