Simplex category
Okay, imagine you have a toy box filled with all sorts of different toys. Now, let's say you want to organize those toys so that all the balls are together, all the dolls are together, and all the blocks are together. This is similar to what the simplex category does, but with math stuff instead of toys.
Just like how you grouped the toys together based on what they were, the simplex category groups mathematical things that are similar together. Specifically, it groups together simple shapes called simplices. These simplices are like the building blocks of geometry and topology.
But the simplex category doesn't just group together simplices. It also looks at how those simplices fit together to create even more complex shapes. It's like if you put some blocks together to make a tower, the simplex category would recognize that the tower is made up of the individual blocks and how they relate to each other.
Overall, the simplex category is a way to organize and understand the relationships between simple mathematical shapes, like how you organized your toys in your toy box.
Just like how you grouped the toys together based on what they were, the simplex category groups mathematical things that are similar together. Specifically, it groups together simple shapes called simplices. These simplices are like the building blocks of geometry and topology.
But the simplex category doesn't just group together simplices. It also looks at how those simplices fit together to create even more complex shapes. It's like if you put some blocks together to make a tower, the simplex category would recognize that the tower is made up of the individual blocks and how they relate to each other.
Overall, the simplex category is a way to organize and understand the relationships between simple mathematical shapes, like how you organized your toys in your toy box.
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