HybridFunctorial Structure and MultiFunctorial Structure
Takaaki Fujita1,∗, Ajoy Kanti Das2
1Independent Researcher, Tokyo, Japan
2Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India
Emails: Takaaki.fujita060@gmail.com; ajoykantidas@gmail.com
Abstract
A Functorial Structure is defined as a covariant functor F : C → Set, assigning sets to objects and functions
to morphisms, ensuring functoriality. 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 compat-
ibility. A MultiFunctorial Structure involves multiple functors indexed by a preorder, coherently related via
natural transformations, forming compatible families with functorial consistency.
Keywords: Functorial Structure; HybridFunctorial Structure; MultiFunctorial Structure