Binary grading of tensors in the rational theory of continuum mechanics

Frame reference, related frames. Transformation of tensors under a change of frame reference system, binary grading of vectors and tensors. Objective tensors of different ranks; types of objectivity: material, spatial and mixed types.
Simple commutative diagrams of objective tensors of one and the same rank and different types of objectivity, transitional tensors, interweaving (intertwining) operators. Tensor processes, representations through introspections (retrospections) and the instant of time, transformation under a change of a frame reference.
Mappings between tensors, types of generalized isotropy. Maps between objective tensors: physically the same and mathematically the same — independent of the reference frame. Frame independence criterion (theorem), special constraints on the mathematical form of the map. Examples. The absence of constraints for Ilyushin-type mappings.
Inductor and package of its conductors (mappings). Ilyushin-type inductor generates a package of conductors of the most general kind. Objective derivatives by time of objective tensor processes are the conductors of the Ilyushin-type inductor — the material derivative by time. Lagrangian and Eulerian representation of objective derivatives.