相关论文: Generic partiality for $\frac{3}{2}$-institutions

Broadly speaking Information theory (IT) assumes no structure of the underlying states. But what about contexts where states do have a clear structure - how should IT cope with such situations? And if such coping is at all possible then -…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

Single-image 3D shape reconstruction is an important and long-standing problem in computer vision. A plethora of existing works is constantly pushing the state-of-the-art performance in the deep learning era. However, there remains a much…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…

Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…

Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger…

We introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Algebras for such a signature are presheaves with an interpretation of every function symbol of the signature, and we describe…

We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…

We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…

We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…

We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…

We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…

In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…

The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…

Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…

This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…

The Grammar of Institutions, or Institutional Grammar, is an established approach to encode policy information in terms of institutional statements based on a set of pre-defined syntactic components. This codebook provides coding guidelines…

Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…

The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…