# Moore hyperrectangles on a space form a strict cubical omega-category with connections

@inproceedings{Brown2009MooreHO, title={Moore hyperrectangles on a space form a strict cubical omega-category with connections}, author={Ronald Brown}, year={2009} }

A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical !-category. This also has the structure of connections in the sense of Brown and Higgins, but cancellation of connections does not hold.

## 12 Citations

A Model Of Type Theory In Cubical Sets With Connections

- Mathematics
- 2014

In this thesis we construct a new model of intensional type theory in the category of cubical sets with connections. To facilitate this we introduce the notion of a nice path object category, a…

A lax symmetric cubical category associated to a directed space (

- Mathematics
- 2010

The recent domain of directed algebraic topology studies 'directed spaces', where paths and homotopies cannot generally be reversed. At the place of the classical fundamental groupoid of a…

The blob complex

- Mathematics
- 2010

Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B_*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT,…

Higher categories, colimits, and the blob complex

- MathematicsProceedings of the National Academy of Sciences
- 2011

The important properties of the blob complex are outlined and the proof of a generalization of Deligne’s conjecture on Hochschild cohomology and the little discs operad to higher dimensions is sketched.

Models of Type Theory Based on Moore Paths

- MathematicsLog. Methods Comput. Sci.
- 2019

A new family of models of intensional Martin-L\"of type theory based on simplicial and cubical sets that can contain more than one element, no matter how great the degree of nesting is, is introduced.

Models of Type Theory Based on Moore Paths

- MathematicsFSCD
- 2017

A new family of models of intensional Martin-L\"of type theory based on simplicial and cubical sets is introduced, notable for avoiding any form of Kan filling condition in the semantics of types.

A higher category of cobordisms and topological quantum field theory

- Mathematics
- 2011

The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners…

28 : 2 Models of Type Theory Based on Moore Paths where

- Computer Science
- 2017

A new family of models of intensional Martin-Löf type theory based on constructive ordered algebra in toposes is introduced, notable for avoiding any form of Kan filling condition in the semantics of types.

A Model of Type Theory in Cubical Sets

- MathematicsTYPES
- 2013

A model of type theory with dependent product, sum, and identity, in cubical sets is presented, and is a step towards a computational interpretation of Voevodsky's Univalence Axiom.

Quantum Fields as Category Algebras

- MathematicsSymmetry
- 2021

By utilizing category algebras and states on categories instead of simply considering categories, this work can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure.

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