Related papers: Negation and Involutive Adjunction
A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism representing the deviation from the Pentagon condition. We uncover a binary tree…
Multi-adjoint logic programming is a general framework with interesting features, which involves other positive logic programming frameworks such as monotonic and residuated logic programming, generalized annotated logic programs, fuzzy…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
We give a theoretical model of conjunctions $E\wedge F$ and implications $E\implies F$ where $F$ is meaningful only when $E$ is true, a situation which is very often encountered in everyday mathematics, and which was already formalized by…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
We first announce our recent result on adjunction and inversion of adjunction. Then we clarify the relationship between our inversion of adjunction and Hacon's inversion of adjunction for log canonical centers of arbitrary codimension.
We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…
In this paper we investigate the categories of braided objects, algebras and bialgebras in a given monoidal category, some pairs of adjoint functors between them and their relations. In particular we construct a braided primitive functor…
This paper focuses on a class of additive perturbations in dynamical systems. An equivalence statement for this construction is discovered, and consequently, a method of checking a notion of positive invariance with perturbation. The…
We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an…
Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general…
Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language…
There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
The categorical compositional distributional model of meaning gives the composition of words into phrases and sentences pride of place. However, it has so far lacked a model of logical negation. This paper gives some steps towards providing…
We prove inversion of adjunction for higher rational singularities.
The assumption that the system Hamiltonian for entangled states is additive is widely used in orthodox quantum no-signalling arguments. It is shown that additivity implies a contradiction with the assumption that the system being studied is…
We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existential elementary doctrines has a left biadjoint that can be…
We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate the mutual influence of conceptual conjunction and negation by measuring the membership…
This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…