arXiv subjects
Publications and source records attributed to Giovanni Marelli.
We show first that derivators can be seen as models of a suitable homotopy limit 2-sketch. After discussing homotopy local $λ$-presentability of the 2-category of derivators, for some appropriate regular cardinal $λ$, as an application we prove that derivators of small presentation are homotopy $λ$-presentable objects.
We explain how categories, and groupoids, can be seen as models for a Lawvere ${\mathfrak Gr}$-theory, where ${\mathfrak Gr}$ is the category of graphs, and show that for Lawvere ${\mathfrak Gr}$-theories finitely presentable models are finitely presentable objects.
Given a complex analytic function f on a Whitney stratified complex analytic variety of complex dimension n, whose real part Re(f) is Morse, we prove the existence of a stratified gradient-like vector field for Re(f) such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimension $m(p)+n-s$ as was conjectured by Goresky and MacPherson.