Category theory; homological algebra Categories, functors, natural transformations Concept
Free category
Summary
The free category on a directed graph has the vertices of the graph as objects and the finite paths of edges as morphisms. Paths are composed by joining them end to end. It is the most general category generated by the graph: no equations between paths hold except those forced by the axioms of a category. It plays for categories the role that the free monoid plays for monoids.
Further reading
About this page
| Tag | THRHFW3SMP |
|---|---|
| URI | m2://THRHFW3SMP |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A10, 18A40 |
| Specializes | Category |
| Same as | |
| Changed | 2 November 2026 |
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