**Date:** October 6 2021

**Summary:** An overview on the applications of category theory to computing; introduces acsets, port graphs, and other applied category theory ideas.

**Keywords:** #bibliography #acsets #graph #theory #category #archive

E. Patterson, O. Lynch, and J. Fairbanks, "Categorical Data Structures for Technical Computing," arXiv:2106.04703 [cs, math], Jun. 2021, Accessed: Sep. 27, 2021. [Online]. Available: http://arxiv.org/abs/2106.04703

**Combinatorial Data** - data stored in a graph

**Attribute data** - the data that would be put into a data frame

Does not record relationships between entities

Analogous to the

`FOREIGN KEY`

concept in SQL

Act as a unifying abstract data type

Particularly useful for graphs and data frames, data structures

Enables creation of novel data structures

The category theory for acsets is well understood

Opens possibility of implementation of

```
- Limits
- Colimits
- Functorial data migration
```

Combinatorial data could be thought of the data that:

```
- Exists solely within a graph structure
- Defines vertices in a graph structure
- Defines edges in a graph structure
- Set of all vertices and set of all edges are isomorphic
- As long as edge-vertex relationships are maintained
```

Attribute data has something concrete that describes it apart from a graph structure

`- Encodes symmetries or relationships in data that are important to that data`

What are the "new data structures" that could be developed with this implementation

Why are attribute data combined in the same structure housing combinatorial data?

With the snippet of

`add_part!`

, what is a "part"?

Zelko, Jacob. *Categorical Data Structures for Technical Computing*. https://jacobzelko.com/10062021162335-ascets-paper. October 6 2021.

CC BY-SA 4.0 Jacob Zelko. Last modified: January 17, 2023.
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