5 papers
Canonical differential calculi via functorial geometrization
Keegan J. Flood, Gabriele Lobbia, Giacomo Tendas
Given a category , we establish sufficient conditions on a faithful isofibration valued in the category of mono…
Quantitative Monoidal Algebra: Axiomatising Distance with String Diagrams
Gabriele Lobbia, Wojciech Różowski, Ralph Sarkis +1
String diagrammatic calculi have become increasingly popular in fields such as quantum theory, circuit theory, probabilistic programming, and machine learning, where they enable re…
Sketches and Classifying Logoi
Ivan Di Liberti, Gabriele Lobbia
Inspired by the theory of classifying topoi for geometric theories, we define rounded sketches and logoi and provide the notion of classifying logos for a rounded sketch. Rounded s…
A finite approach to representable multicategories and related structures
Gabriele Lobbia
It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to repres…
Some Remarks on the Interchange in Gray-categories
Nicola Di Vittorio, Gabriele Lobbia
We prove a generalised interchange equality for 3-cells in a Gray-category, i.e. we show that it still holds modulo the unique isomorphism given by the Gray-categorical pasting the…