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- W4287754149 abstract "The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $mathcal{F}$-quotients in a category $mathbf{C}$, which are relativized to a faithful functor $mathcal{F}colon mathbf{C} to mathbf{D}$. The isomorphism theorems of universal algebras generalize to this setting, and we additionally find important links between $mathcal{F}$-quotients in the concrete category of first-order structures, and quotients defined for model-theoretic equivalence classes. By first working in this categorical setting, some quotient-related results for first-order structures can be naturally obtained. In particular, we are able to prove some isomorphism theorems in the context of model theory directly from their corresponding categorical isomorphism theorems." @default.
- W4287754149 created "2022-07-26" @default.
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- W4287754149 date "2020-06-21" @default.
- W4287754149 modified "2023-09-26" @default.
- W4287754149 title "On functor-quotients and their isomorphism theorems" @default.
- W4287754149 doi "https://doi.org/10.48550/arxiv.2006.11720" @default.
- W4287754149 hasPublicationYear "2020" @default.
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