**Title:** Differential bundles as functors

**Abstract:** Differential bundles are the generalisation of vector bundles in tangent categories. Following an idea by Michael Ching, we will consider lax morphisms of tangent categories, functors between tangent categories preserving the tangent structure, and show that they induce differential bundles under certain conditions. Then we will continue to show that the categories of differential bundles in a tangent category X with additive/linear morphisms are equivalent to the category of tangent functors from the category of free commutative monoids into X.