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We construct super-version of Quantum Representation Theory. The quadraticsuper-algebras and operations on them are described. We also describe someimportant monoidal functors. We proved that the monoidal category of gradedsuper-algebras with Manin product is coclosed relative to the subcategory offinitely generated quadratic super-algebras. The super-version of the$(A,B)$-Manin matrices is introduced and related with the quadraticsuper-algebras. We define a super-version of quantum representations and ofquantum linear actions, relate them to each other and describe them by thesuper-Manin matrices. Some operations on quantum representations/quantum linearactions are described. We show how the classical representations lift to thequantum level.

Quantum Representation Theory and Manin matrices II: super case