Related papers: Accessible set endofunctors are universal

A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…

Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…

We show that each rigid monoidal category A over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from A to tensor categories. Each of the universal tensor categories classifies…

There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors induce an equivalence of homotopy theories. This result…

We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are invariantly universal. This notion from the theory of Borel…

Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal)…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

For every adjunction of stable $\infty$-categories -- or more generally, in any locally stable $(\infty,2)$-category -- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence,…

The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…

We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global…

The Grothendieck universe axiom asserts that every set is a member of some set-theoretic universe U that is itself a set. One can then work with entities like the category of all U-sets or even the category of all locally U-small…

We give a short proof that the Yoneda embedding is natural for $\infty$-categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embedding, is contractible.

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…

Consider the intrinsic fundamental group \`a la Grothendieck of a linear category using connected gradings. In this article we prove that any full convex subcategory is incompressible, in the sense that the group map between the…

We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…

We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to…

We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding…

We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of $C^*$- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence…

This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…

The functor that takes a manifold to its configuration category exhibits a type of full faithfulness in some cases.