Update about.md

_pages/about.md

@@ -10,10 +10,10 @@ redirect_from:
 
 My email address is mmlme@leeds.ac.uk
 
-I am about to conclude my PhD in category theory at the School of Mathematics of the University of Leeds, UK, under the supervision of Nicola Gambino. I visited the University of Genova, Italy, from August 2023 to October 2023. Before, I visited the University of Manchester, UK, from September 2022 to August 2023.
+I am about to conclude my PhD in category theory at the School of Mathematics of the University of Leeds, UK, under the supervision of Nicola Gambino. I visited the University of Genova, Italy, from August 2023 to October 2023. Before that, I visited the University of Manchester, UK, from September 2022 to August 2023.
 
 My main research interests are category theory and its applications to logic, geometry and computer science. More precisely, I have a keen interest in fibrations and the Grothendieck construction, 2-category theory, enriched category theory and 2-categorical elementary topoi.
 
-During my PhD, I have been working on 2-classifiers, that are a 2-categorical generalization of subobject classifiers and can be thought of as Grothendieck constructions inside a 2-category. I proved that 2-categorical Grothendieck topoi have a 2-classifier. This also involved reducing the conditions of a 2-classifier to dense generators, studying colimits in 2-dimensional slices, an indexed Grothendieck construction and an essential conicalization of weighted 2-limits.
+My PhD thesis contributes to expand 2-dimensional elementary topos theory. In particular, I present a novel technique of reduction of the study of 2-classifiers to dense generators. I then apply it to generalize to dimension 2 the fundamental result that Grothendieck topoi are elementary topoi. In order to reach my main theorems, I produced an original calculus of colimits in 2-dimensional slices and an indexed version of the Grothendieck construction.
 
 I am very passionate about research and I am a positive person who always smiles. I value love, truth and communication. In my free time, I like travelling as well as creating and playing board games.