HybridFunctorial Structure and MultiFunctorial Structure

Abstract

A Functorial Structure is defined as a covariant functor ? : C → Set, assigning sets to objects and functions to morphisms, ensuring functoriality [1]. In this paper, we introduce and formally define two new concepts: the HybridFunctorial Structure and the MultiFunctorial Structure. A HybridFunctorial Structure combines two functors on the same category, linked by a natural transformation, ensuring consistent pushforward compatibility. A MultiFunctorial Structure involves multiple functors indexed by a preorder, coherently related via natural transformations, forming compatible families with functorial consistency