Related papers: Factorization systems induced by weak distributive…
We have studied the effect of weak randomness on q-state Potts models for q > 4 by measuring the central charges of these models using transfer matrix methods. We obtain a set of new values for the central charges and then show that some of…
Distributive laws give a way of combining two algebraic structures expressed as monads; in this paper we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches,…
This article presents three characterizations of the weak factorization systems on finitely complete categories that interpret intensional dependent type theory with Sigma-, Pi-, and Id-types. The first characterization is that the weak…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the…
Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…
A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…
A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For…
We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…
An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer…
The weak localization (WL) contribution to the two-level correlation function is calculated for two-dimensional disordered conductors. Our analysis extends to the nondiffusive (ballistic) regime, where the elastic mean path is of order of…
We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between…
We study a special class of weakly associative algebras: the symmetric Leibniz algebras. We describe the structure of the commutative and skew symmetric algebras associated with the polarization-depolarization principle. We also give a…
Distributive laws are a standard way of combining two monads, providing a compositional approach for reasoning about computational effects in semantics. Situations where no such law exists can sometimes be handled by weakening the notion of…
We describe the weak polynomial identities of the Jordan algebra of symmetric $2\times 2$ matrices over a field of characteristic zero. The corresponding weak verbal ideal is generated by the standard identity of degree four and the…
We describe the canonical weak distributive law $\delta \colon \mathcal S \mathcal P \to \mathcal P \mathcal S$ of the powerset monad $\mathcal P$ over the $S$-left-semimodule monad $\mathcal S$, for a class of semirings $S$. We show that…
The weak factorization theorem for birational maps is used to prove that for all nonnegative i the ith mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a "virtual Betti number" beta_i defined for…
Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…
In this paper we introduce the class of weak Heyting Brouwer algebras (WHB-algebras, for short). We extend the well known duality between distributive lattices and Priestley spaces, in order to exhibit a relational Priestley-like duality…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…