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math.AT2024
Model structures for diagrammatic -categories
Clémence Chanavat, Amar Hadzihasanovic
Diagrammatic sets admit a notion of internal equivalence in the sense of coinductive weak invertibility, with similar properties to its analogue in strict -categories. We constr…
math.CT2024
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…
math.AT2024
Diagrammatic sets as a model of homotopy types
Clémence Chanavat, Amar Hadzihasanovic
Diagrammatic sets are presheaves on a rich category of shapes, whose definition is motivated by combinatorial topology and higher-dimensional diagram rewriting. These shapes includ…