Monoidal Functor

A monoidal functor is a mathematical concept describing a structure-preserving map between two categories equipped with a way to combine objects and morphisms (called a monoidal structure). Think of it as a function that not only translates elements from one system to another but also respects how these elements combine. It ensures that combining objects in the source category corresponds to combining their images in the target category, maintaining the structure intact. This concept helps mathematicians understand how different mathematical systems relate when their composition rules are preserved through this mapping.