Related papers: On $\infty$-Categories
A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are…
We define a convenient $\infty$-operad parametrizing modules over commutative algebras in $\infty$-categories.
These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.
The notion of a $v$-palindrome is recently introduced by the author. Later, the author defined the notion of the type of a $v$-palindrome $n$ with respect to a number $m$ which can be repeatedly concatenated to form $n$. We prove that this…
We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…
The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
In this paper, we give the introduction to the Hodge-Iwasawa Theory introduced by the author. After that we will give some well-defined extensions to the already shaped framework established in our previous work.
We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our…
Interoperability is crucial for modern scientific advancement, yet its fragmented definitions across domains hinder researchers' ability to effectively reap the rewards. This paper proposes a new, universal definition by tracing the…
We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal…