Self-Curvature and Non-Naturality in 2-Term L∞-Algebras

This paper introduces the notion of self-action on 2-term L∞-algebras and defines a corresponding self-curvature as a cohomological obstruction to functoriality. The construction provides a higher analogue of curvature in deformation theory and measures the failure of compatibility between homotopy-coherent endomorphisms and morphisms of L∞-algebras. We show that self-curvature vanishes if and only if the self-action extends to a compatible L∞-morphism. In addition, we introduce a notion of non-naturality, which captures obstructions not detected by cohomology alone. This framework connects deformation theory, obstruction theory, and higher categorical structures, situating self-curvature as a functorial obstruction invariant in homotopical algebra.