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 migrationCombinatorial 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 maintainedAttribute data has something concrete that describes it apart from a graph structure
- Encodes symmetries or relationships in data that are important to that dataWhat 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.