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Internal Categories and Factorisation Systems

Ranchod, Sanjiv
(2022)

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Ranchod044419012022.pdf
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Details

Supervisors
Gran, Marino
Degree label
Mobilité entrante en sciences
Abstract
We motivate and define internal categories and related structures. We consider and prove Brown and Spencer's equivalence between internal categories in Grp and crossed modules, and Patchkoria's equivalence between Schreier internal categories in Mon and crossed semimodules. We provide an overview of the theory of factorisation systems and introduce the notion of an internal factorisation system, as well as prove properties thereof. We consider how internal categories and internal factorisation systems manifest in Mal'tsev varieties.