Let $ G be a countable discrete group and consider nonsingular Bernoulli shift action \curvearrowright \prod_{g\in }(\{0,1\},\mu_g)$ with two base points. When is exact, under certain finiteness assumption on the measures $\{\mu_g\}_{g\in }$, we construct boundary for crossed product C$^*$-algebra that admits some commutativity amenability in sense of Ozawa's bi-exactness. As consequence, obtai...

The distributive laws of ring theory are fundamental equalities in algebra. However, recently the study Yang-Baxter equation, many algebraic structures with alternative “distributive” were defined. In an effort to these “left distributive” and interaction they entail on structures, Brzezi?ski introduced skew left trusses semi-trusses. particular class semi-trusses is very wide, since it contain...

An algebraically exact category is one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Adámek, Lawvere and Rosický: they characterised them as the categories with small lim...

The purpose of this paper is to give a new presentation of some of the main results concerning Landweber exactness in the context of the homotopy theory of stacks. We present two new criteria for Landweber exactness over a flat Hopf algebroid. The first criterion is used to classify stacks arising from Landweber exact maps of rings. Using as extra input only Lazard’s theorem and Cartier’s class...

Article history: Received 19 April 2013 Received in revised form 7 August 2013 Available online 25 November 2013 Communicated by J. Adámek MSC: 18F10; 18A32; 18D05 We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on obj...

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the...

The exact unification type of an equational theory is based on a new preorder on substitutions, called the exactness preorder, which is tailored towards transferring decidability results for unification to disunification. We show that two important results regarding the unification type of commutative theories hold not only for the usual instantiation preorder, but also for the exactness preord...

In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are quadrature rules with multiple nodes and the maximal degree of exactness in some functional spaces that are different from the space of algebraic polynomial. For that purpose we present a generaliz...