Filtered Frobenius Algebras in Monoidal Categories

Abstract We develop filtered-graded techniques for algebras in monoidal categories with the main goal of establishing a categorical version Bongale’s 1967 result: filtered deformation Frobenius algebra over field is as well. Toward goal, we first construct associated graded functor, building on prior works Ardizzoni and Menini, Galatius et al., Gwillian Pavlov. Next, produce equivalent conditions an rigid category to be terms existence form; this builds work Fuchs Stigner. These two results independent interest are then used achieve our goal. As application result, show that any exact module symmetric finite tensor $\mathcal {C}$ represented by {C}$. Several directions further investigation also proposed.