Dendroidal set
So, imagine you have a toy house with lots of rooms. Each room has a different shape and size. Now, imagine that you have little toys that are shaped like people, animals, and objects. These toys can move around the rooms and do different things, like sit in chairs, play on the floor, or climb up stairs.
Now, let's say that each toy has a different color. The blue toys might be the people, the red toys might be the animals, and the yellow toys might be the objects. And let's say that each room has a different color too. The blue room might be a bedroom, the red room might be a living room, and the yellow room might be a kitchen.
This is kind of like a dendroidal set! A dendroidal set is a way of describing how different objects (toys) can move around in a special kind of structure (the toy house). But instead of colors, we use different shapes and sizes to describe the different objects and structure.
In a dendroidal set, the special structure is called a dendroid, which is kind of like a tree. The different parts of the dendroid (branches, leaves, etc.) have different shapes and sizes, just like the rooms in the toy house. And the objects that move around in the dendroidal set are called simplices, which are basically just shapes (like triangles, squares, and circles) that can fit inside the different parts of the dendroid.
So when we say "dendroidal set," we're talking about a way of describing how these simplices (shapes) can move around in this special type of structure (the dendroid). And just like in the toy house example, each simplex (shape) can be labeled with different information, like colors or labels. This is how we keep track of everything in a dendroidal set!
Now, let's say that each toy has a different color. The blue toys might be the people, the red toys might be the animals, and the yellow toys might be the objects. And let's say that each room has a different color too. The blue room might be a bedroom, the red room might be a living room, and the yellow room might be a kitchen.
This is kind of like a dendroidal set! A dendroidal set is a way of describing how different objects (toys) can move around in a special kind of structure (the toy house). But instead of colors, we use different shapes and sizes to describe the different objects and structure.
In a dendroidal set, the special structure is called a dendroid, which is kind of like a tree. The different parts of the dendroid (branches, leaves, etc.) have different shapes and sizes, just like the rooms in the toy house. And the objects that move around in the dendroidal set are called simplices, which are basically just shapes (like triangles, squares, and circles) that can fit inside the different parts of the dendroid.
So when we say "dendroidal set," we're talking about a way of describing how these simplices (shapes) can move around in this special type of structure (the dendroid). And just like in the toy house example, each simplex (shape) can be labeled with different information, like colors or labels. This is how we keep track of everything in a dendroidal set!