Simplification for Graph-like Objects

Fuente: arXiv

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Autore principale:	Grilliette, Will
Natura:	Preprint
Pubblicazione:	2020
Soggetti:	Combinatorics Category Theory 05C20, 05C65, 18A25, 18A40
Accesso online:	Acceder al recurso
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_version_	1866911778536947712
author	Grilliette, Will
author_facet	Grilliette, Will
contents	The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the functor-structured category. Seated in categorical terms, simplification can be dualized to "antisimplification", which manifests as removal of isolated vertices and loose edges.
format	Preprint
id	arxiv_https___arxiv_org_abs_2012_08772
institution	arXiv
publishDate	2020
record_format	arxiv
spellingShingle	Simplification for Graph-like Objects Grilliette, Will Combinatorics Category Theory 05C20, 05C65, 18A25, 18A40 The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the functor-structured category. Seated in categorical terms, simplification can be dualized to "antisimplification", which manifests as removal of isolated vertices and loose edges.
title	Simplification for Graph-like Objects
topic	Combinatorics Category Theory 05C20, 05C65, 18A25, 18A40
url	https://arxiv.org/abs/2012.08772

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

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