Related papers: A Small Observation on Co-categories

In categories of linear relations between finite dimensional vector spaces, composition is well-behaved only at pairs of relations satisfying transversality and monicity conditions. A construction of Wehrheim and Woodward makes it possible…

Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…

In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is…

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.

We prove that a category which is symmetric (relaxed) monoidal closed, (small) complete, well-powered and has a small cogenerating family, is cocomplete.

In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind…

We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…

Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…

Inspired by recent work on the categorical semantics of dependent type theories, we investigate the following question: When is logical structure (crucially, dependent-product and subobject-classifier structure) induced from a category to…

There are various adjunctions between model (co-)slice and slice categories. We characterize when these adjunctions are Quillen equivalences. As an application, a triangle equivalence between the stable category of a Frobenius category and…

The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…

To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

In this short note we prove that two definitions of (co)ends in $\infty$-categories, via twisted arrow $\infty$-categories and via $\infty$-categories of simplices, are equivalent. We also show that weighted (co)limits, which can be defined…

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

In this work, we establish a categorification of the classical Dold-Kan correspondence in the form of an equivalence between suitably defined $\infty$-categories of simplicial stable $\infty$-categories and connective chain complexes of…

Coclass theory can be used to define infinite families of finite p-groups of a fixed coclass. It is conjectured that the groups in one of these infinite families all have isomorphic mod-p cohomology rings. Here we prove that almost all…

We establish a Dwyer-Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable (infinity,1)-categories. This implies that the underlying quasicategories…

Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that…

We introduce a 3-dimensional categorical structure which we call intercategory. This is a kind of weak triple category with three kinds of arrows, three kinds of 2-dimensional cells and one kind of 3-dimensional cells. In one dimension, the…