Spaceability of sets of non-injective maps

Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces A of maps from an arbitraty set to a sequence space, that, for every 0 f A, the subset of A of non-injective maps contains an infinite dimensional subspace of A containing f. We provide aplications of the main result to spaces of linear operators between quasi-Banach spaces, to spaces of linear operators belonging to an operator ideal, and, in the nonlinear setting, to linear spaces of homogeneous polynomials and to linear spaces of vector-valued Lispshitz functions on metric spaces.