8 papers
A strengthened -categorical pasting theorem
Clémence Chanavat
We extend Campion's pasting theorem for -categories to a larger class of polygraphs, called the directed complexes with frame-acyclic molecules. It follows, for instan…
Equivalences in diagrammatic sets
Clémence Chanavat, Amar Hadzihasanovic
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict -categories, admit an internal notion of equivalence in the sense of coinductive weak…
A Compositional Account of Generalized Reversible Computing
Clémence Chanavat, Priyaa Varshinee Srinivasan
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned…
Homotopy theory of stricter -categories
Clémence Chanavat
We make strict -categories even stricter by requiring they satisfy higher exchange laws governed by Hadzihasanovic's theory of regular directed complexes. We study the first pro…
Semi-strictification of -categories
Clémence Chanavat, Amar Hadzihasanovic
We prove the first equivalence between a weak non-algebraic model and a semi-strict algebraic model of -categories. This takes the form of a natural semi-strictificati…
Gray products of diagrammatic -categories
Clémence Chanavat
For each , diagrammatic sets admit a model structure whose fibrant objects are the diagrammatic - categories. They also support a not…