Term substitution induces an associative operation on the free objects of any equational variety. In the case of left distributivity, the construction can be extended to any monogenic structure.

in this paper, using pre-semi-open l-sets and their inequality, a new notion of ps-compactness is introduced in l-topological spaces, where l is a complete de morgan algebra. this notion does not depend on the structure of the basis lattice l and l does not need any distributivity.

We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.

1The particle ina follows gradable expressions and adds meanings such as ‘high in quantity/quality’ or ‘high in degree’ to the expression. Also, these meanings entail a degree of surprise, that is, quantity/quality/degree/extent is above expectation of the speaker. measure phrase such that the speaker entails that the height of Philip is way above the standard of comparison, i.e., Philip is ver...

We show that a constraint language with compatible Jónnson terms (i.e. associated with an algebra generating a congruence distributive variety) defines a Constraint Satisfaction Problem solvable by the local consistency checking algorithm.

We prove that for any Set-endofunctor F the category SetF of F -coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever SetF has finite products.

We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The selfdistributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Ya...

Many separation logics support fractional permissions to distinguish between read and write access a heap location, for instance, allow concurrent reads while enforcing exclusive writes. Fractional extend composite assertions such as (co)inductive predicates magic wands by allowing those be multiplied fraction. Typical logic proofs require that this multiplication has three key properties: it n...

Every dialogue category comes equipped with a continuation monad defined by applying the negation functor twice. In this paper, we advocate that this double negation monad should be understood as part of a larger parametric monad (or a lax action) with parameter taken in the opposite of the dialogue category. This alternative point of view has one main conceptual benefit: it reveals that the st...