Simplicially enriched category
A simplicially enriched category is a way to organize and compare things, like toys, by using shapes called simplices instead of just counting them.
Imagine you have a toy box with different blocks of different shapes, sizes and colors. An ordinary category would just tell you which blocks are there and how they relate to each other. But a simplicially enriched category would give each block a shape, like a triangle, a square or a pentagon.
Then, instead of just saying that one block is bigger or smaller than the other, the simplicially enriched category would use these shapes to compare them in a more precise way. For example, it might say that the triangle block is more like the square block than the pentagon block, because they share more common features.
In the end, using a simplicially enriched category allows you to not just count things, but to organize and compare them in a more sophisticated and nuanced way.
Imagine you have a toy box with different blocks of different shapes, sizes and colors. An ordinary category would just tell you which blocks are there and how they relate to each other. But a simplicially enriched category would give each block a shape, like a triangle, a square or a pentagon.
Then, instead of just saying that one block is bigger or smaller than the other, the simplicially enriched category would use these shapes to compare them in a more precise way. For example, it might say that the triangle block is more like the square block than the pentagon block, because they share more common features.
In the end, using a simplicially enriched category allows you to not just count things, but to organize and compare them in a more sophisticated and nuanced way.