Galois connection
Imagine you have two boxes, box A and box B. Box A has some toys and box B has some tools. You can think of these boxes as sets of objects.
Now, a galois connection is like having two people, let's call them Alice and Bob, who can go back and forth between these boxes. Alice takes some toys from box A and tries to find matching tools in box B. Bob does the opposite and takes some tools from box B and tries to find matching toys in box A.
The idea is that when Alice and Bob each return from their respective box, they compare what they found. If Alice found a tool that matches her toy, and Bob found a toy that matches his tool, they have established a relationship between the two boxes. That's what we call an "adjunction" or a "galois connection".
This can be helpful in mathematics when we have two different sets with some kind of relationship between them. We can use a galois connection to help us understand that relationship and translate concepts between the two sets.
Now, a galois connection is like having two people, let's call them Alice and Bob, who can go back and forth between these boxes. Alice takes some toys from box A and tries to find matching tools in box B. Bob does the opposite and takes some tools from box B and tries to find matching toys in box A.
The idea is that when Alice and Bob each return from their respective box, they compare what they found. If Alice found a tool that matches her toy, and Bob found a toy that matches his tool, they have established a relationship between the two boxes. That's what we call an "adjunction" or a "galois connection".
This can be helpful in mathematics when we have two different sets with some kind of relationship between them. We can use a galois connection to help us understand that relationship and translate concepts between the two sets.