Globular: an online proof assistant for higher-dimensional rewriting

This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their construction with a point-and-click interface, and performs type checking to prevent incorrect rewrites. Hosted on the web, it has a low barrier to use, and allows hyperlinking of formalized proofs directly from research papers. It allows the formalization of proofs from logic, topology and algebra which are not formalizable by other methods, and we give several examples.

[1]  Yves Lafont,et al.  Algebra and Geometry of Rewriting , 2007, Appl. Categorical Struct..

[2]  Piotr Pstrkagowski,et al.  On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis , 2014, 1411.6691.

[3]  Kenneth A. Perko,et al.  On the classification of knots , 1974 .

[4]  Nicolai Reshetikhin,et al.  Quantum Groups , 1993 .

[5]  A. Joyal,et al.  The geometry of tensor calculus, I , 1991 .

[6]  Samuel Mimram,et al.  Towards 3-Dimensional Rewriting Theory , 2014, Log. Methods Comput. Sci..

[7]  Yves Guiraud,et al.  Polygraphs for termination of left-linear term rewriting systems , 2007, ArXiv.

[8]  Aaron D. Lauda,et al.  Higher-Dimensional Algebra V: 2-Groups , 2003 .

[9]  Tom Leinster.  A Survey of Definitions of n-Category , 2001 .

[10]  John W. Barrett,et al.  Gray categories with duals and their diagrams , 2012, 1211.0529.

[11]  Stephen Lack,et al.  A Coherent Approach to Pseudomonads , 2000 .

[12]  Ralf Hinze,et al.  Kan Extensions for Program Optimisation Or: Art and Dan Explain an Old Trick , 2012, MPC.

[13]  Shahn Majid,et al.  A Quantum Groups Primer , 2002 .

[14]  Aleks Kissinger,et al.  Quantomatic: A proof assistant for diagrammatic reasoning , 2015, CADE.

[15]  Jamie Vicary,et al.  Data structures for quasistrict higher categories , 2016, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[16]  Joachim Kock.  Frobenius Algebras and 2D Topological Quantum Field Theories: Frobenius algebras , 2003 .