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Autor:
MacAdam, Benjamin
Ehresmann's introduction of differentiable groupoids in the 1950s may be seen as a starting point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis uses tangent
Externí odkaz:
http://arxiv.org/abs/2301.00305
Autor:
MacAdam, Benjamin
A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced differential bundle
Externí odkaz:
http://arxiv.org/abs/2007.11708
Autor:
Cockett, Robin, Cruttwell, Geoffrey, Gallagher, Jonathan, Lemay, Jean-Simon Pacaud, MacAdam, Benjamin, Plotkin, Gordon, Pronk, Dorette
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differentia
Externí odkaz:
http://arxiv.org/abs/1910.07065
Autor:
Burke, Matthew, MacAdam, Benjamin
We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to the Yang-B
Externí odkaz:
http://arxiv.org/abs/1904.06594
Autor:
MacAdam, Benjamin
Ehresmann's introduction of differentiable groupoids in the 1950s may be seen as a starting point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis uses tangent
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5f5b9e0ca05c4e3ee8cb8cdcf9b2d11
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