Simplicial localization
Okay, so imagine you have a big bucket of Legos. And you want to build something cool, like a spaceship. But sometimes the Legos don't fit together perfectly, and it's hard to build the spaceship you want.
That's kind of like how mathematicians work with shapes called simplicial complexes. Sometimes, it's hard to fit them together perfectly to figure out what they look like. But there's a trick called simplicial localization that helps make it easier.
Basically, simplicial localization means you take a simplicial complex and make some parts of it act like they're all stuck together, even if they're not. It's like if you have a bunch of Legos that are almost touching, but not quite, and you glue them together so they can't move around independently anymore.
By doing this, you simplify the shape and make it easier to understand. It's like now you have a spaceship that's made from bigger blocks of Legos, and you can see how everything fits together better.
So, simplicial localization helps mathematicians study simplicial complexes by making them simpler and easier to work with. And just like how you can build a cooler spaceship with bigger, more organized Legos, mathematicians can understand complex shapes better with simplicial localization.
That's kind of like how mathematicians work with shapes called simplicial complexes. Sometimes, it's hard to fit them together perfectly to figure out what they look like. But there's a trick called simplicial localization that helps make it easier.
Basically, simplicial localization means you take a simplicial complex and make some parts of it act like they're all stuck together, even if they're not. It's like if you have a bunch of Legos that are almost touching, but not quite, and you glue them together so they can't move around independently anymore.
By doing this, you simplify the shape and make it easier to understand. It's like now you have a spaceship that's made from bigger blocks of Legos, and you can see how everything fits together better.
So, simplicial localization helps mathematicians study simplicial complexes by making them simpler and easier to work with. And just like how you can build a cooler spaceship with bigger, more organized Legos, mathematicians can understand complex shapes better with simplicial localization.