Related papers: Algebraic weighted colimits
We define and study the notions of ribbon dioperads and modular ribbon properads. We give a Lie algebra structure on the colimit total object and the limit total object of a ribbon dioperad, and we give a norm map between them. We give a…
A weak entwining structure in a 2-category K consists of a monad t and a comonad c, together with a 2-cell relating both structures in a way that generalizes a mixed distributive law.A weak entwining structure can be characterized as a…
The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory that algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes…
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these…
We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…
In this work, we prove a generalization of Quillen's Theorem A to 2-categories equipped with a special set of morphisms which we think of as weak equivalences, providing sufficient conditions for a 2-functor to induce an equivalence on…
Interest in weak cubical n-categories arises in various contexts, in particular in topological field theories. In this paper, we describe a concept of double bicategory, namely a strict model of the theory of bicategories in Bicat. We show…
We arrange morphisms and comorphisms of sites as the horizontal and vertical cells of a double category of sites; using the formalism of extensions and restrictions of presheaves, we explains how one can define a sheafification double…
In the previous three papers in this series, [WKO1]-[WKO3] (arXiv:1405.1956, arXiv:1405.1955, and to appear), Z. Dancso and I studied a certain theory of "homomorphic expansions" of "w-knotted objects", a certain class of knotted objects in…
In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad…
The weak boundedness property associated with a standard alpha-fractional Calderon-Zygmund operator and a weight pair is good-lambda controlled by the testing conditions and the Muckenhoupt and energy side conditions. As a consequence,…
This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory -- categorifying the classical theory of categories enriched in a monoidal category -- up to a description of the free…
We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects,…
We study the question of dualizability in higher Morita categories of locally presentable tensor categories and braided tensor categories. Our main results are that the 3-category of rigid tensor categories with enough compact projectives…
Using the machinery of weak fibration categories due to Schlank and the first author, we construct a convenient model structure on the pro-category of separable $C^*$-algebras $\mathrm{Pro}(\mathtt{SC^*})$. The opposite of this model…
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary…
A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various versions of this notion have already been explored; our goal…
We develop the theory of tricategorical limits and colimits, and show that they can be modelled up to biequivalence via certain homotopically well-behaved limits and colimits enriched over the monoidal model category $\mathbf{Gray}$ of…
In this article, the author analyses distributive and mixed distributive laws and some of their equivalences through the use of 2-adjunctions of the type $\Adj$-$\Mnd$. As far as the distributive laws are concerned, the equivalence between…