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Bibliographic Details
Main Author:	Zhu, Chenchang
Format:	Preprint
Published:	2008
Subjects:	Differential Geometry Category Theory
Online Access:	https://arxiv.org/abs/0801.2057
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A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model)
by: Lackman, Joshua
Published: (2023)

The Adjoint Representation of a Higher Lie Groupoid
by: Trentinaglia, Giorgio
Published: (2023)

Duals of Higher Vector Spaces
by: Ronchi, Stefano, et al.
Published: (2024)

Hypercovers in Differential Geometry
by: Glass, Cheyne, et al.
Published: (2026)

On the normal functor in the category of smooth vector bundles
by: Kohal, Quentin Karegar Baneh
Published: (2026)

Discrete differential geometry in homotopy type theory
by: Langmead, Greg
Published: (2025)

Internal geometry and functors between sites
by: Waldorf, Konrad
Published: (2024)

The holonomy Lie $\infty$-groupoid of a singular foliation I
by: Laurent-Gengoux, Camille, et al.
Published: (2025)

Quasi-coherent sheaves and D-modules in Derived Differential Supergeometry
by: Carchedi, David
Published: (2025)

Relative Stability Conditions on Triangulated Categories
by: Liu, Bowen, et al.
Published: (2024)

Groupoid Cardinality and Random Permutations
by: Baez, John C.
Published: (2024)

Moduli stacks of quiver bundles with applications to Higgs bundles
by: Azam, Mahmud, et al.
Published: (2024)

A Model of Type Theory in Groupoid Assemblies
by: Agwu, Anthony
Published: (2025)

The Diffeological Čech-de Rham Obstruction
by: Minichiello, Emilio
Published: (2024)

Diffeological Principal Bundles and Principal Infinity Bundles
by: Minichiello, Emilio
Published: (2022)

A Simplicial Approach to Higher Geometric Quantization
by: Zhang, Qian
Published: (2026)

Towards Riemannian diffeology
by: Kuribayashi, Katsuhiko, et al.
Published: (2025)

On the structure of étale fibrations of $L_\infty$-bundles
by: Behrend, Kai, et al.
Published: (2023)

Bicategories of Action Groupoids
by: Farsi, Carla, et al.
Published: (2022)

Groupoids, imaginaries and internal covers
by: Hrushovski, Ehud
Published: (2006)

Categorical and geometric methods in statistical, manifold, and machine learning
by: Lê, Hông Vân, et al.
Published: (2025)

Random Surfaces and Higher Algebra
by: Lee, Darrick, et al.
Published: (2023)

Internal absolute geometry I: desingularization
by: Bohlen, Karsten
Published: (2021)

Synthetic G-jet-structures in modal homotopy type theory
by: Cherubini, Felix
Published: (2018)

Groupoidal Realizability for Intensional Type Theory
by: Speight, Sam
Published: (2024)

Representability in non-linear elliptic Fredholm analysis
by: Pardon, John
Published: (2023)

Gaugings of Groupoids, Strings in Shadows, and Emergent Poisson $σ$-Models
by: Suszek, Rafał R.
Published: (2026)

Thin homotopy and the signature of piecewise linear surfaces
by: Bischoff, Francis, et al.
Published: (2025)

Partial Groupoid Actions on Smooth Manifolds
by: Marín, Víctor, et al.
Published: (2023)

Differential graded manifolds of finite positive amplitude
by: Behrend, Kai, et al.
Published: (2023)

TQFTs and quantum computing
by: Azam, Mahmud, et al.
Published: (2022)

Categorical generalization of BF theory coupled to gravity
by: López-Hernández, A. D., et al.
Published: (2024)

Analytic Linearization and Holomorphic Extensions of Proper Groupoids
by: Fernandes, Rui Loja, et al.
Published: (2025)

On Multiplicative Weightings for Lie Groupoids and Lie Algebroids
by: Hudson, Daniel
Published: (2025)

The Surface Signature and Rough Surfaces
by: Lee, Darrick
Published: (2024)

Symplectic double groupoids and the generalized Kähler potential
by: Álvarez, Daniel, et al.
Published: (2024)

Adjusted Connections I: Differential Cocycles for Principal Groupoid Bundles with Connection
by: Fischer, Simon-Raphael, et al.
Published: (2024)

Stereotype Dualities in Geometry
by: Akbarov, S. S.
Published: (2023)

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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; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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