Spectral sequence of homotopy colimits
Imagine we have a bunch of different shapes, like circles, squares, and triangles. We want to figure out how they are connected to each other, like which ones can fit inside other ones and how they fit together.
To do this, we can use something called homotopy colimits. It's like taking all the shapes and smooshing them together into one big shape, where the connections between them are all preserved.
But sometimes this can get really complicated and we need a way to break it down into smaller, more manageable pieces. This is where the spectral sequence comes in.
Think of the spectral sequence like a map. It helps us keep track of how the shapes are connected to each other as we smoosh them together. We start with the shapes in their original form and then use the spectral sequence to see how they change as they get smooshed together.
It's kind of like following a trail of breadcrumbs to figure out how everything fits together. Each breadcrumb represents a small change that happens as we put the shapes together, and by following the trail, we can see the bigger picture of how everything is connected.
So, in short, the spectral sequence of homotopy colimits is like a map that helps us understand how different shapes are connected to each other as we smoosh them together. It breaks down the process into smaller steps so we can understand it better.
To do this, we can use something called homotopy colimits. It's like taking all the shapes and smooshing them together into one big shape, where the connections between them are all preserved.
But sometimes this can get really complicated and we need a way to break it down into smaller, more manageable pieces. This is where the spectral sequence comes in.
Think of the spectral sequence like a map. It helps us keep track of how the shapes are connected to each other as we smoosh them together. We start with the shapes in their original form and then use the spectral sequence to see how they change as they get smooshed together.
It's kind of like following a trail of breadcrumbs to figure out how everything fits together. Each breadcrumb represents a small change that happens as we put the shapes together, and by following the trail, we can see the bigger picture of how everything is connected.
So, in short, the spectral sequence of homotopy colimits is like a map that helps us understand how different shapes are connected to each other as we smoosh them together. It breaks down the process into smaller steps so we can understand it better.