Related papers: A Generalised Exactness Structure for Sets

Certain results involving "higher structures" are not currently accessible to computer formalization because the prerequisite $\infty$-category theory has not been formalized. To support future work on formalizing $\infty$-category theory…

We generalize the correspondence between theories and monads with arities of arXiv:1101.3064 to $\infty$-categories. Additionally, we introduce the notion of complete theories that is unique to the $\infty$-categorical case and provide a…

In the present work, a natural sequel to \cite{MaPi1}, we further discuss the existence of adjunctions between categories of institutions and of $\pi$-institutions. This is done at both a foundational and an applied level. Firstly, we…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

Let X_1 and X_2 be schemes of finite type over a field of characteristic 0. Let Q be an object in the category D-mod(X_1\times X_2) and consider the functor F:D-mod(X_1)->Dmod(X_2) defined by Q. Assume that F admits a right adjoint also…

We develop the theory of recollements in a stable $\infty$-categorical setting. In the axiomatization of Beilinson, Bernstein and Deligne, recollement situations provide a generalization of Grothendieck's "six functors" between derived…

Given a representation of a C*-algebra, thought of as an abstract collection of physical observables, together with a unit vector, one obtains a state on the algebra via restriction. We show that the Gelfand-Naimark-Segal (GNS) construction…

Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relationship with torsion theories, Galois theory, homology and factorisation systems. It is shown how…

We study the bicategory of Landau-Ginzburg models, which has potentials as objects and matrix factorisations as 1-morphisms. Our main result is the existence of adjoints in this bicategory and a description of evaluation and coevaluation…

We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy…

Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general structures such as bicategories and virtual double…

We define a coherent adjunction in a strict $3$-category and we use string diagrams to show that any adjunction can be extended to a coherent adjunction in an essentially unique way.

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…

Conjugation, or Legendre transformation, is a basic tool in convex analysis, rational mechanics, economics and optimization. It maps a function on a linear topological space into another one, defined in the dual of the linear space by…

For any 0-cell $B$ in a 2-category $\Bc$ we introduce the notion of adjoint algebra $\adj_B$. This is an algebra in the center of $\Bc$. We prove that, if $\ca$ is a finite tensor category, this notion applied to the 2-category of…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

We propose a treatment of coordination based on the concepts of functor, argument and subcategorization. Its formalization comprises two parts which are conceptually independent. On one hand, we have extended the feature structure…