41 citations · 48 across the 14 of their papers we have counts for
15 papers
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…
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…
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…
Acyclicity conditions on pasting diagrams
Amar Hadzihasanovic, Diana Kessler
We study various acyclicity conditions on higher-categorical pasting diagrams in the combinatorial framework of regular directed complexes. We present an apparently weakest acyclic…
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…
A model for the coherent walking -equivalence
Amar Hadzihasanovic, Félix Loubaton, Viktoriya Ozornova +1
We prove that a certain -category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking -equivalence. Further, app…
Combinatorics of higher-categorical diagrams
Amar Hadzihasanovic
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding r…
Higher-dimensional subdiagram matching
Amar Hadzihasanovic, Diana Kessler
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two s…
Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting
Amar Hadzihasanovic, Diana Kessler
We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpret…
The smash product of monoidal theories
Amar Hadzihasanovic
The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as…
Diagrammatic sets and rewriting in weak higher categories
Amar Hadzihasanovic
We revisit Kapranov and Voevodsky's idea of spaces modelled on combinatorial pasting diagrams, now as a framework for higher-dimensional rewriting and the basis of a model of weak…
Representable diagrammatic sets as a model of weak higher categories
Amar Hadzihasanovic
Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose…
Weak units, universal cells, and coherence via universality for bicategories
Amar Hadzihasanovic
Poly-bicategories generalise planar polycategories in the same way as bicategories generalise monoidal categories. In a poly-bicategory, the existence of enough 2-cells satisfying…
The algebra of entanglement and the geometry of composition
Amar Hadzihasanovic
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this f…
A Topological Perspective on Interacting Algebraic Theories
Amar Hadzihasanovic
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic the…