This chapter discusses non-technical account of some ideas in the theory of∞-categories,
as originally introduced by Boardman–Vogt in their study of homotopy-invariant algebraic …

We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a
family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This …

Motivated by traces of matrices and Euler characteristics of topological spaces, we expect
abstract traces in a symmetric monoidal category to be “additive”. When the category is …

We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-
category of substitudes of Day and Street (2003), and that the Feynman categories of …

The theory of derivators enhances and simplifies the theory of triangulated categories. In this
article a notion of fibered (multi-) derivator is developed, which similarly enhances fibrations …

We study the representation theory of Dynkin quivers of type A in abstract stable homotopy
theories, including those associated to fields, rings, schemes, differential-graded algebras …

Generalised BGP Reflection Functors via the Grothendieck Construction | International
Mathematics Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford …

We generalize the construction of reflection functors from classical representation theory of
quivers to arbitrary small categories with freely attached sinks or sources. These reflection …

Stable derivators provide an enhancement of triangulated categories as is indicated by the
existence of canonical triangulations. In this paper we show that exact morphisms of stable …

We show that variants of the classical reflection functors from quiver representation theory
exist in any abstract stable homotopy theory, making them available for example over …