mathlib documentation

algebra.category.FinVect.limits

forget₂ (FinVect K) (Module K) creates all finite limits. #

And hence FinVect K has all finite limits.

Future work #

After generalising FinVect to allow the ring and the module to live in different universes, generalize this construction so we can take limits over smaller diagrams, as is done for the other algebraic categories.

@[protected, instance]
def FinVect.category_theory.limits.pi_obj.finite_dimensional {k : Type v} [field k] {J : Type v} [fintype J] (Z : J → Module k) [∀ (j : J), finite_dimensional k (Z j)] :
finite_dimensional k ( λ (j : J), Z j)
@[protected, instance]

Finite limits of finite finite dimensional vectors spaces are finite dimensional, because we can realise them as subobjects of a finite product.