Related papers: Difference-restriction algebras with operators
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…
We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the…
Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…
Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor…
We extend the equivalence by Cockett and Garner between restriction monoids and ample categories to the setting of Boolean range semigroups which are non-unital one-object versions of range categories. We show that Boolean range semigroups…
We develop an obstruction theory for the extension of truncated minimal $A$-infinity bimodule structures over truncated minimal $A$-infinity algebras. Obstructions live in far-away pages of a (truncated) fringed spectral sequence of…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds.…
We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…
As left adjoint to the dual algebra functor, Sweedler's finite dual construction is an important tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the dual algebra functor, which exists over…
A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and…
We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…
Tangent categories provide a categorical axiomatization of the tangent bundle. There are many interesting examples and applications of tangent categories in a variety of areas such as differential geometry, algebraic geometry, algebra, and…
Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…
We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed…
Extensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental in proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions,…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In our recent article, we have extended de Vries duality to completely regular spaces by generalizing de Vries algebras…
Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article…