Related papers: The category of Waldhausen categories as a closed …

We prove that the 2-category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2-subcategory of the 2-category of closed multicategories.

We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we…

We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…

We give a simple representation of all elements in K_1 of a Waldhausen category and prove relations between these representatives which hold in K_1.

In this survey we discuss some combinatorial aspects of higher cluster categories.

In this work we develop some categorical aspects of the double structure of a module.

This paper is concerned with some well-known Ljusternik-Schnirelmann categories. We desire to find some links and relations among them. This has been done by using the concepts of precategoty, T-collection and closure of a category.

Utilizing simplicial Waldhausen theory, we prove that the geometric realization of the topologized category of bounded chain complexes over complex numbers (resp. real numbers) is an infinite loop space that represents connective complex…

In this paper we describe how to give a particular global category of rings and modules the structure of a relaxed multi category, and we describe an algebra in this relaxed multi category such that vertex algebras appear as such algebras.

We study a categorical construction called the cobordism category, which associates to each Waldhausen category a simplicial category of cospans. We prove that this construction is homotopy equivalent to Waldhausen's…

This is a condensed overview of the formal theory of monads in a 2-category. We also define two double categories of monads in a 2-category, extending Lack and Street's 2-categories of monads.

A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.

In [7], we introduced the category of chain bundles with examples and established its significance. Here we shall describe certain categories which we call the category of chains in the chain bundle category and discuss some interesting…

Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…

In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.

The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.

We define a skew-closed structure for Gray-categories extending the mapping space construction of the author.

Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.

Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…