Related papers: Higher presentable categories and limits

Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…

We define a functor which takes in an $(\infty,1)$-category and outputs an $(\omega,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in…

We introduce the notion of an accessible $\infty$-cosmos and prove that these include the basic examples of $\infty$-cosmoi and are stable under the main constructions. A consequence is that the vast majority of known examples of…

We show, assuming PD, that every complete finitely axiomatized second order theory with a countable model is categorical, but that there is, assuming again PD, a complete recursively axiomatized second order theory with a countable model…

We show that the homotopy theories of differential graded categories and $\mathrm{A}_\infty$-categories over a field are equivalent at the $(\infty,1)$-categorical level. The results are corollaries of a theorem of Canonaco-Ornaghi-Stellari…

We consider $(\infty,d)$-categories in the limit $d\to \infty$ via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare the two resulting $(\infty,1)$-categories of…

We construct an adjunction between $m$-categories internal to $(\infty,n)$-categories, called $(n,m)$-double $\infty$-categories, and filtrations $A_0\to \dots\to A_m$ where for all $i<m$, $A_i$ is a $(n+i)$-category. We show that this…

Univalence was first defined in the setting of homotopy type theory by Voevodsky, who also (along with Kapulkin and Lumsdaine) adapted it to a model categorical setting, which was subsequently generalized to locally Cartesian closed…

Pursuing the notions of ambidexterity and higher semiadditivity as developed by Hopkins and Lurie, we prove that the span $\infty$-category of $m$-finite spaces is the free $m$-semiadditive $\infty$-category generated by a single object.…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

We introduce $\infty$-type theories as an $\infty$-categorical generalization of the categorical definition of type theories introduced by the second named author. We establish analogous results to the previous work including the…

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…

We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…

We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty$-categorical exact completion (resp. hypercompletion) of an abelian category recovers the connective half of its bounded (resp. unbounded)…

A sketch is a category equipped with specified collections of cones and cocones. Its models are functors to the category of sets that send the distinguished cones and cocones to limit cones and colimit cocones, respectively. Sketches…

We show that the vanishing of higher derived limits of the system $\mathbf{A}_\kappa$ implies the additivity of strong homology on the class of locally compact metric spaces of weight at most $\kappa$, thereby establishing a converse to a…

For a group G with trivial center there is a natural embedding of G into its automorphism group, so we can look at the latter as an extension of the group. So an increasing continuous sequence of groups, the automorphism tower, is defined,…

This paper reformulates Goodwillie calculus of $\infty$-categories including non-presentable $\infty$-categories. In the case of presentable $\infty$-categories our definition is equivalent to Heuts's~\cite{Heuts2018} work. As an…

One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial…

Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become…