Paper: Fat Cell Structures and Generalized Algebraic Theories (at LICS 2026)

Authors: Xu Huang Carlo Angiuli

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.58

Abstract

We give a new syntax-independent account of finitely-presented generalized algebraic theories (GATs) as finite cell complexes in the category of categories with families (CwFs), in which GATs are constructed by successive pushouts along the CwF morphisms generically postulating a sort, an operation, or an equation. Inspired by the fat small object argument of Makkai, Rosický, and Vokřínek, we introduce fat GAT presentations, thereby allowing infinite presentations with non-linear dependency structure. Then, motivated by wanting our GATs to self-describe, we extend presentations to admit infinitary arities, including infinitely deep dependency chains. Finally, we verify that these generalized GATs satisfy expected semantic properties including Frey’s Gabriel–Ulmer duality.

BibTeX

  @InProceedings{HuangAngiuli-FatCellStructuresan,
    author = 	 {Xu Huang and Carlo Angiuli},
    title = 	 {Fat Cell Structures and Generalized Algebraic Theories},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {58:1--58:27},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.58}
  }