It is shown that a singular equivalence induced by tensoring with suitable complex of bimodules defines Morita type level, in the sense Wang. This result applied to homological ideals and idempotents produce new reduction techniques for testing properties syzygy-finite injectives generation finite dimensional algebras over field.

Most aggregation queries contain both group-by and join operators, and spend a significant amount of time evaluating these two expensive operators. Merging them into one operator (the groupjoin) significantly speeds up query execution. We introduce two main equivalences to allow for the merging and prove their correctness. Furthermore, we show experimentally that these equivalences can signific...

We show that adequate semantics can be provided for imperative higher order concurrent languages simply using syntactical nal coalgebras. In particular we investigate and compare various behavioural equivalences on higher order processes deened by nality using hyper-sets and c.m.s.'s. Correspondingly, we derive various coinduction and mixed induction-coinduction proof principles for establishin...

What is a homotopy theory T? – Examples of homotopy theories (Tpair presentation) – The homotopy category Ho(T) – Examples of homotopy categories – Model category: (C, E) with extras – Examples of model categories (C, E) – Dividends from a model category structure on (C, E) – Equivalences between homotopy theories – T(C, E) ∼ T(C′, E ′) for model categories – Examples of equivalences between ho...

It is well known that the category KHaus of compact Hausdorff spaces is dually equivalent to the category KRFrm of compact regular frames. By de Vries duality, KHaus is also dually equivalent to the category DeV of de Vries algebras, and so DeV is equivalent to KRFrm, where the latter equivalence can be described constructively through Booleanization. Our purpose here is to lift this circle of ...

The categorical formulation of the Eilenberg-Watts calculus relates, for any pair finite categories M and N, Fun^{le}(N,M) Fun^{re}(N,M) linear left or right exact functors Deligne product \bar N \boxtimes by adjoint equivalences. We establish a variant this case that are module over tensor category. This provides in particular canonical explicitly computable equivalences between (or, more gene...

Both discounting and optimism can induce impatient behavior in the present. This paper derives equivalences between classes of discount functions and classes of (possibly erroneous) sets of beliefs in a standard intertemporal choice context. We find that strong assumptions about beliefs are generically necessary for identification of the discount function.

Many database queries can be formulated in terms of expressions whose operands represent tables of information (relations) and whose operators are the relational operations select, project, and join. This paper studies the equivalence problem for these relational expressions, with expression optimization in mind. A matrix, called a tableau, is proposed as a natural representative for the value ...

The aim of this paper is to find the finest ‘observable’ and ‘implementable’ equivalence on concurrent processes. This is a part of a larger programme to develop a theory of observable processes where semantics of processes are based on locally and finitely observable process behaviour, and all process constructs are allowed, provided their operational meaning is defined by realistically implem...