Matches in SemOpenAlex for { <https://semopenalex.org/work/W4383468765> ?p ?o ?g. }
Showing items 1 to 47 of
47
with 100 items per page.
- W4383468765 abstract "This thesis captures the ongoing development of twisted cubes, which is a modification of cubes (in a topological sense) where its homotopy type theory does not require paths or higher paths to be invertible. My original motivation to develop the twisted cubes was to resolve the incompatibility between cubical type theory and directed type theory. The development of twisted cubes is still in the early stages and the intermediate goal, for now, is to define a twisted cube category and its twisted cubical sets that can be used to construct a potential definition of (infinity, n)-categories. The intermediate goal above leads me to discover a novel framework that uses graph theory to transform convex polytopes, such as simplices and (standard) cubes, into base categories. Intuitively, an n-dimensional polytope is transformed into a directed graph consists 0-faces (extreme points) of the polytope as its nodes and 1-faces of the polytope as its edges. Then, we define the base category as the full subcategory of the graph category induced by the family of these graphs from all n-dimensional cases. With this framework, the modification from cubes to twisted cubes can formally be done by reversing some edges of cube graphs. Equivalently, the twisted n-cube graph is the result of a certain endofunctor being applied n times to the singleton graph; this endofunctor (called twisted prism functor) duplicates the input, reverses all edges in the first copy, and then pairwisely links nodes from the first copy to the second copy. The core feature of a twisted graph is its unique Hamiltonian path, which is useful to prove many properties of twisted cubes. In particular, the reflexive transitive closure of a twisted graph is isomorphic to the simplex graph counterpart, which remarkably suggests that twisted cubes not only relate to (standard) cubes but also simplices." @default.
- W4383468765 created "2023-07-07" @default.
- W4383468765 creator A5065795896 @default.
- W4383468765 date "2023-07-03" @default.
- W4383468765 modified "2023-10-18" @default.
- W4383468765 title "Twisted Cubes and their Applications in Type Theory" @default.
- W4383468765 doi "https://doi.org/10.48550/arxiv.2307.01327" @default.
- W4383468765 hasPublicationYear "2023" @default.
- W4383468765 type Work @default.
- W4383468765 citedByCount "0" @default.
- W4383468765 crossrefType "posted-content" @default.
- W4383468765 hasAuthorship W4383468765A5065795896 @default.
- W4383468765 hasBestOaLocation W43834687651 @default.
- W4383468765 hasConcept C114614502 @default.
- W4383468765 hasConcept C118615104 @default.
- W4383468765 hasConcept C145691206 @default.
- W4383468765 hasConcept C156772000 @default.
- W4383468765 hasConcept C18903297 @default.
- W4383468765 hasConcept C2777299769 @default.
- W4383468765 hasConcept C33923547 @default.
- W4383468765 hasConcept C53051483 @default.
- W4383468765 hasConcept C86803240 @default.
- W4383468765 hasConceptScore W4383468765C114614502 @default.
- W4383468765 hasConceptScore W4383468765C118615104 @default.
- W4383468765 hasConceptScore W4383468765C145691206 @default.
- W4383468765 hasConceptScore W4383468765C156772000 @default.
- W4383468765 hasConceptScore W4383468765C18903297 @default.
- W4383468765 hasConceptScore W4383468765C2777299769 @default.
- W4383468765 hasConceptScore W4383468765C33923547 @default.
- W4383468765 hasConceptScore W4383468765C53051483 @default.
- W4383468765 hasConceptScore W4383468765C86803240 @default.
- W4383468765 hasLocation W43834687651 @default.
- W4383468765 hasOpenAccess W4383468765 @default.
- W4383468765 hasPrimaryLocation W43834687651 @default.
- W4383468765 hasRelatedWork W1568620904 @default.
- W4383468765 hasRelatedWork W1975040408 @default.
- W4383468765 hasRelatedWork W1990980885 @default.
- W4383468765 hasRelatedWork W1996256832 @default.
- W4383468765 hasRelatedWork W2099246938 @default.
- W4383468765 hasRelatedWork W2123195153 @default.
- W4383468765 hasRelatedWork W2147422606 @default.
- W4383468765 hasRelatedWork W2953085781 @default.
- W4383468765 hasRelatedWork W3024548395 @default.
- W4383468765 hasRelatedWork W4287169834 @default.
- W4383468765 isParatext "false" @default.
- W4383468765 isRetracted "false" @default.
- W4383468765 workType "article" @default.