Computational Categorical Algebra with Catlab

James Fairbanks
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Abstract

A vast swath of computation and computer science theory takes place on combinatorial data structures, which are often presented as variations on the theme of graphs. Catlab.jl is a Julia package for computational category theory, which includes an implementation of C-Sets, also known as copresheafs or category actions. C-Sets always form an adhesive category and can be used for general rewriting systems. This talk will present the theory and implementation of C-Sets along with some examples. In particular, Colored Graphs and String Diagrams (syntax for symmetric monoidal categories) will be shown.

Date
Friday, May 7, 2021 15:00 Europe/Paris
Event
GReTA seminar

Further information:

Catlab.jl is a framework for applied and computational category theory, written in the Julia language. Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory. (https://github.com/AlgebraicJulia/Catlab.jl)
Catlab.jl is a framework for applied and computational category theory, written in the Julia language. Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory. (https://github.com/AlgebraicJulia/Catlab.jl)

Some references discussed during the Q&A session after the talk:

  • mentioned by A. Corradini: J.W. Gray, The category of sketches as a model for algebraic semantics, Contemp. Math. 92 (1989) 109-135.
  • mentioned by R. Heckel: Corradini A., Groβe-Rhode M., Heckel R. (1999) An Algebra of Graph Derivations Using Finite (co—) Limit Double Theories, Springer LNCS, vol 1589. https://doi.org/10.1007/3-540-48483-3_7
.GReTA-seminar
James Fairbanks
James Fairbanks
Assistant Professor in Computer Science

James Fairbanks, Ph.D., earned his B.S. in Mathematics at the University of Florida and his Ph.D at the Georgia Institute of Technology in Computational Science and Engineering. He studied under the supervision of Professor David A. Bader, while supported by the National Defense Science and Engineering Graduate (NDSEG) Fellowship.

He then worked at the Georgia Tech Research Institute on Data Analysis and High Performance Computing as applied to scientific computing and data science problems in healthcare. social science, epidemiology, biology, and physics problems. His work focuses on using programming language theory and algebraic techniques for designing and developing large scale software for technical computing problems.