Category-vector space analogy
The is a striking, albeit informal, correspondence between the basic concepts of category theory and linear algebra. The following table, based on 2011. Introduction to representation theory, ยง7.6, is a summary.
| Category theory | Linear algebra |
|---|---|
| category | vector space |
| hom-set | nondegenerate bilinear form |
| opposite category | opposite inner product |
| ground field | |
| full subcategory | nondegenerate subspace |
| functor | linear map |
| presheaf | linear form |
| Yoneda lemma | nondegeneracy |
| representable functor | representable form |
| adjoint functor | adjoint operator |
#state/tidy | #lang/en | #SemBr