
Models for ∞categories. Notes for a talk I gave for a seminar in Higher Category Theory at UWO. I give here a survey of complete Segal spaces, simplicial and relative categories as presentations of ∞categories.
A brief survey on Kan Extensions. Notes for a talk I gave in a student learning group at UWO. The title is pretty much selfexplanatory.
Homotopical Structures in Dependent Type Theory. Written project for a course in Categorical Logic I took during Fall 2015 at the University of Western Ontario. Given a dependent type theory with identity types $\mathbb{T}$, we show how to endow the syntactic category of $\mathbb{T}$ with a weak factorization system and with a fibrationcategory structure. If $\mathbb{T}$ also has rules for a suitable higher inductive context, one can pass this fibration category structure to a premodel category structure. Our main references are [GG08], [Gar09], [Lum11] and [AKL15].
A GiraudType Theorem for Model Topoi. My Master thesis. Following the unpublished work of C. Rezk, Toposes and homotopy toposes, we present a formulation of the notion of model topos, intended as a modelcategorical version of the classical concept of Grothendieck topos. Such a definition is sensible enough to establish a Giraudtype theorem for model topoi. There is a little gap still present in some proofs of Chapter 6 (cfr footnote 2 at page 139 and footnotes from 3 to 5 in the following pages), on which I may try to work further at some point.
Localization Theory in Triangulated Categories: a (brief, incomplete and probably superficial) overview. A short journey into the subject, coming from an essay I submitted as part of the application for a PhD position. I spend here few words about localization theory in categories and in triangulated categories and give some connections with recollements, torsion pairs and the telescope conjecture. This text is nothing more than a humble, minuscule drop in the mare magnum of the subject, but someone may perhaps find something useful in it.
Homotopy (Co)limits: a brief survey. Notes for a talk introducing homotopy (co)limits in model categories, given at the Algebraic Topology Student Seminar, organized by the Radboud Topology Group at the Radboud University Nijmegen (Netherlands). We present here a short overview of possible different definitions for the notions of homotopy limits and homotopy colimits in the context of model categories, also providing suitable (and hopefully enough) context to compare them and show their equivalence when this comparison makes sense. We focus in particular on three distinct approaches, namely the one involving derived functor, the homotopical approach and the simplicial version.
Aggiunzioni in Topologia (in Italian). Notes for a talk on some examples of adjunctions in Topology, given to peer students with little background in category theory.
Updated by Marco Vergura, Oct 24th, 2018.