Higher-order operad

Okay, let’s imagine you are playing with Lego blocks. You know how to build a tower by stacking single Lego bricks on top of each other. This is called a first-order operation because it only involves one type of block.

But what if you want to build something more complicated, like a car or a plane? You need different types of blocks and you need to assemble them in a certain way to make it work. This is called a higher-order operation because it involves more than one type of block.

Similarly, an operad is a mathematical tool that allows you to combine operations of different kinds. A first-order operad would be like stacking Lego bricks, but a higher-order operad would be like building more complex structures using different types of blocks.

For example, let’s say you want to create a recipe for baking a cake. You need to combine different steps, like mixing ingredients, preheating the oven, and decorating the cake. An operad can help you organize these steps into a coherent sequence.

In summary, a higher-order operad is a mathematical tool that allows you to combine operations of different kinds to create more complex structures, just like building with different types of Lego blocks.