A Journey from Graphs to Generalized Sketches


In the talk we present the Generalized Sketch Formalism à la Makkai/Diskin as a straightforward and quite natural generalization of specification formalisms based on graphs and graph transformations.
We discuss why traditional Ehresmann Sketches are not fully adequate for the formalization of Software Models and argue in favor of Generalized Sketches. Ehresmann Sketches utilize only the properties commutative, limit or colimit, respectively, while we are allowed to work with arbitrary “user defined” properties in Generalized Sketches. Makkai proposed Sketch Implications as a tool to axiomatize the meaning of “user defined” properties and we elucidate that especially limit and colimit properties can be expressed by means of Sketch Implications. On the other side, we can utilize Sketch Implications as a tool to describe the structure of Software Models.
Compared to Graph Transformations, Sketch Transformations give us a more refined and expressive tool at hand to formalize Model Transformations. It looks like, however, that only the use of cospan transformation rules instead of the traditional span transformation rules would enable us to derive full advantage of sketches.

Friday, April 21, 2023 15:00 Europe/Paris
GReTA seminar
Note: This is a joint event with the working group “Catégories supérieures, polygraphes et homotopie” at IRIF, Université Paris Cité. Before this talk, the speaker will give a theory tutorial on generlized sketches (starting from 14:00 CEST), with an abstract and details on how to attend available here: https://www.irif.fr/~greta/event/2023-apr-21-CT/
Zoom registration: click here! Please consider joining the meeting already within the 15min prior to the start of the seminar to ensure your setup is functioning properly. You may connect with either the Zoom web or Zoom desktop clients.

Please note that the meeting will be recorded and live-streamed to YouTube:

Uwe Wolter
Uwe Wolter

Uwe E. Wolter is associate professor at the University of Bergen, Norway. He received his PhD degree in 1989 from the Technical University Magdeburg, Germany. He was awarded with the Medal of Honour from the East-German Society of Mathematics for the best PhD thesis of the year. He held positions at Humboldt-University Berlin and Technical University Berlin before joining the Department of Informatics at the University of Bergen in 2000.