# Citings — Category Theory

## Primary

- Mac Lane, S. (1971). *Categories for the Working Mathematician*. Springer. Ch. I §1 (category definition, laws); Ch. I §5 (iso/mono/epi); Ch. II §1 (functors); Ch. II §4 (natural transformations); Ch. IV §1 (adjunctions); XII.3 (2-categories).
- Awodey, S. (2010). *Category Theory* (2nd ed.). Oxford University Press. Uses "arrow" as primary term for morphism.
- Bénabou, J. (1967). "Introduction to Bicategories." *Lecture Notes in Mathematics* 47. Springer. First systematic treatment of weak 2-categories.
- Leinster, T. (2004). *Higher Operads, Higher Categories*. LMS Lecture Note Series 298. Cambridge University Press. Modern n-category reference.

## Related ontology literature

- Gruber, T. (1993). "A Translation Approach to Portable Ontology Specifications." *Knowledge Acquisition* 5(2): 199–220. §5 KAS — "ontology = formally-named relations", grounding the "every concept is named" requirement.
- Smith, B., Ceusters, W., Klagges, B., Köhler, J., Kumar, A., Lomax, J., Mungall, C., Neuhaus, F., Rector, A. L., & Rosse, C. (2005). "Relations in Biomedical Ontologies." *Genome Biology* 6(5): R46 (OBO Relation Ontology). Source for the `Kind` requirement on every morphism.
- Lambek, J., & Scott, P. J. (1986). *Introduction to Higher Order Categorical Logic*. Cambridge University Press. Links category theory to typed logic — supplementary for the Curry-Howard framing used in pr4xis's Axiom/Verdict API.
- Spivak, D. I. (2012). "Functorial Data Migration." *Information and Computation* 217: 31–51. Category-theoretic foundation for schema categories as used in pr4xis's ontology registry.
