相关论文: Calculating limits and colimits in pro-categories

We describe a cocompact model for the classifying space for proper actions of the mapping class group of a surface with punctures and boundary components. Our construction relies on a known model for the case of a closed surface and uses an…

The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriated framework to specify and integrate learning processes, data transformation processes and…

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example $\mathcal E_\infty$-coalgebras, $\mathcal A_\infty$-coalgebras,…

The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

In this paper we prove that various quasi-categories whose objects are $\infty$-categories in a very general sense are complete: admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a…

While any infimum in a poset can also be computed as a supremum, and vice versa, categorical limits and colimits do not always approximate each other. If I approach a point from below, and you approach it from above, then we will surely…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent…

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 offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…

We study the interaction between the notions of filteredness, fractions and fibrations in the theory of bicategories, generalizing classical results for categories. We give an explicit formula for filtered pseudo-colimits of categories…

We show that a map between fibrant objects in a closed model category is a weak equivalence if and only if it has the right homotopy extension lifting property with respect to all cofibrations. The dual statement holds for maps between…

We contribute to the theory of (homotopy) colimits inside homotopy type theory. The heart of our work characterizes the connection between (graph-indexed) colimits in a type universe and colimits in coslices of the universe, called coslice…

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…