105 citations · 325 across the 15 of their papers we have counts for
16 papers
Computads for weak -categories as an inductive type
Christopher J. Dean, Eric Finster, Ioannis Markakis +2
We give a new description of computads for weak globular -categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads,…
Semisimple Field Theories Detect Stable Diffeomorphism
David Reutter, Christopher Schommer-Pries
Extending the work of the first author, we introduce a notion of semisimple topological field theory in arbitrary even dimension and show that such field theories necessarily lead…
Zigzag normalisation for associative -categories
Lukas Heidemann, David Reutter, Jamie Vicary
The theory of associative -categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant,…
Minimal nondegenerate extensions
Theo Johnson-Freyd, David Reutter
We prove that every slightly degenerate braided fusion category admits a minimal nondegenerate extension, and hence that every pseudo-unitary super modular tensor category admits a…
A 3-categorical perspective on G-crossed braided categories
Corey Jones, David Penneys, David Reutter
A braided monoidal category may be considered a -category with one object and one -morphism. In this paper, we show that, more generally, -categories with one object and $…
A Type Theory for Strictly Unital -Categories
Eric Finster, David Reutter, Alex Rice +1
We use type-theoretic techniques to present an algebraic theory of -categories with strict units. Starting with a known type-theoretic presentation of fully weak -c…
Semisimple 4-dimensional topological field theories cannot detect exotic smooth structure
David Reutter
We prove that semisimple 4-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented s…
Uniqueness of unitary structure for unitarizable fusion categories
David Reutter
We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified pol…
High-level methods for homotopy construction in associative -categories
David Reutter, Jamie Vicary
A combinatorial theory of associative -categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising…
Fusion 2-categories and a state-sum invariant for 4-manifolds
Christopher L. Douglas, David J. Reutter
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented s…
Shaded tangles for the design and verification of quantum circuits
David J. Reutter, Jamie Vicary
We give a scheme for interpreting shaded tangles as quantum circuits, with the property that if two shaded tangles are ambient isotopic, their corresponding computational effects a…
The Morita theory of quantum graph isomorphisms
Benjamin Musto, David Reutter, Dominic Verdon
We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum…
A compositional approach to quantum functions
Benjamin Musto, David Reutter, Dominic Verdon
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use t…
A classical groupoid model for quantum networks
David J. Reutter, Jamie Vicary
We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our a…
Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
David Reutter, Jamie Vicary
We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in t…
Biunitary constructions in quantum information
David J. Reutter, Jamie Vicary
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previo…