相关论文: A sketchy note on enriched homotopical topologies …

We provide a definition of enrichment that applies to a wide variety of categorical structures, generalizing Leinster's theory of enriched $T$-multicategories. As a sample of newly enrichable structures, we describe in detail the examples…

We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…

For an arbitrary symmetric monoidal $\infty$-category $\mathcal{V}$, we define the factorization homology of $\mathcal{V}$-enriched $(\infty,1)$-categories over (possibly stratified) 1-manifolds and study some of its basic properties. In…

In this paper we construct a cofibrantly generated model category structure on the category of all small symmetric multicategories enriched in simplicial sets.

We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for…

Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…

It is proved that the projective model structure of the category of topologically enriched diagrams of topological spaces over a topologically enriched locally contractible small category is Quillen equivalent to the standard Quillen model…

We introduce the notion of an enriched set, as an abstraction of enriched categories, and a category of enriched sets. The set of enriched sets is itself described as a set enriched over the category of enriched sets. We introduce a method…

The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for…

We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the philosophy of classical (enriched) Segal categories. We study…

Enriched curves have been studied over algebraically closed fields by Main\`o ([Mai98]) and recently over general base schemes in [BH19]. In this paper, we study enriched curves from a logarithmic viewpoint: we give a succinct definition of…

This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of the enriched hom-objects need not be in bijection with the…

We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dg- and…

Mackey functors provide the coefficient systems for equivariant cohomology theories. More generally, enriched presheaf categories provide a classification and organization for many stable model categories of interest. Changing enrichments…

We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a simple but flexible method for constructing…

We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our previous work. This recovers several known examples of…

This work is the first one in a series, in which we develop a mathematical theory of enriched (braided) monoidal categories and their representations. In this work, we introduce the notion of the $E_0$-center ($E_1$-center or $E_2$-center)…

We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.

We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…