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- W4287123257 abstract "Many mathematical objects can be represented as functors from finitely-presented categories $mathsf{C}$ to $mathsf{Set}$. For instance, graphs are functors to $mathsf{Set}$ from the category with two parallel arrows. Such functors are known informally as $mathsf{C}$-sets. In this paper, we describe and implement an extension of $mathsf{C}$-sets having data attributes with fixed types, such as graphs with labeled vertices or real-valued edge weights. We call such structures acsets, short for attributed $mathsf{C}$-sets. Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames. They also encompass more elaborate graph-like objects such as wiring diagrams and Petri nets with rate constants. We develop the mathematical theory of acsets and then describe a generic implementation in the Julia programming language, which uses advanced language features to achieve performance comparable with specialized data structures." @default.
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- W4287123257 date "2022-12-28" @default.
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- W4287123257 title "Categorical Data Structures for Technical Computing" @default.
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- W4287123257 doi "https://doi.org/10.32408/compositionality-4-5" @default.
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