4 citations · 5 across the 8 of their papers we have counts for
10 papers
Semi-strict 4-categories as enriched categories
John Bourke, Gabriele Lobbia
We introduce several flavours of semi-strict 4-category as enriched categories. This is done using the framework of enrichment over skew monoidal categories of Gray-categories and…
The symmetric skew monoidal structure of Gray-categories
John Bourke, Gabriele Lobbia
In previous work, we constructed a closed skew monoidal structure on the category of Gray-categories and Gray-functors whose internal hom Psd(A, B) captures pseudomaps and pseudo-t…
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…
A skew approach to enrichment for Gray-categories
John Bourke, Gabriele Lobbia
It is well known that the category of Gray-categories does not admit a monoidal biclosed structure that models weak higher-dimensional transformations. In this paper, the first of…
KZ-pseudomonads and Kan Injectivity
Ivan Di Liberti, Gabriele Lobbia, Lurdes Sousa
We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category , we show that every set of morphisms ind…
Distributive laws for relative monads
Gabriele Lobbia
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category . In order…