75 citations · 544 across the 41 of their papers we have counts for
10 papers · 1 filter
Posetal Diagrams for Logically-Structured Semistrict Higher Categories
Chiara Sarti, Jamie Vicary
We now have a wide range of proof assistants available for compositional reasoning in monoidal or higher categories which are free on some generating signature. However, none of th…
A layout algorithm for higher-dimensional string diagrams
Calin Tataru, Jamie Vicary
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layo…
A Syntax for Strictly Associative and Unital -Categories
Eric Finster, Alex Rice, Jamie Vicary
We present the first definition of strictly associative and unital -category. Our proposal takes the form of a type theory whose terms describe the operations of such struc…
Traced Monoidal Categories as Algebraic Structures in Prof
Nick Hu, Jamie Vicary
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categorie…
A Type Theory for Strictly Associative Infinity Categories
Eric Finster, Alex Rice, Jamie Vicary
Many definitions of weak and strict -categories have been proposed. In this paper we present a definition for -categories with strict associators, but which is othe…
Traced monoidal categories as algebraic structures in
Nick Hu, Jamie Vicary
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categorie…
The Word Problem for Braided Monoidal Categories is Unknot-Hard
Antonin Delpeuch, Jamie Vicary
We show that the word problem for braided monoidal categories is at least as hard as the unknotting problem. As a corollary, so is the word problem for Gray categories. We conjectu…
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…
Data structures for quasistrict higher categories
Krzysztof Bar, Jamie Vicary
We present new data structures for quasistrict higher categories, in which associativity and unit laws hold strictly. Our approach has low axiomatic complexity compared to traditio…
Completeness of dagger-categories and the complex numbers
Jamie Vicary
The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of phy…