English

Bicategories of Lax Fractions

Category Theory 2026-02-17 v2

Abstract

The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was generalised to bicategories by Pronk. We extend these constructions by presenting a calculus of lax fractions for 2-categories that formally turns given morphisms into left adjoint right inverses and given pseudo-commutative squares into Beck-Chevalley squares.

Keywords

Cite

@article{arxiv.2507.12044,
  title  = {Bicategories of Lax Fractions},
  author = {Graham Manuell and Lurdes Sousa},
  journal= {arXiv preprint arXiv:2507.12044},
  year   = {2026}
}

Comments

60 pages + 62 pages of appendices; added full proofs and made many small edits