Monoid action
A monoid action is like playing with blocks. Let's say you have a set of blocks with different shapes and colors.
A monoid is like a set of rules on how you can play with these blocks. For example, you could have a rule that says you can only stack the blocks in a certain order.
An action is when you actually play with the blocks using these rules. So let's say you have three blocks: a red circle, a blue square, and a yellow triangle.
If your monoid rule is to stack the blocks in alphabetical order of their shape names, you could stack them like this:
1. Yellow triangle on the bottom
2. Red circle on top of the triangle
3. Blue square on top of the circle
This is an example of a monoid action because you used a set of rules (the monoid) to perform an action (stacking the blocks) in a certain way.
Another example of a monoid action could be rotating the blocks. Let's say you have the same three blocks, but this time your monoid rule is to rotate the blocks in order of their colors.
You could rotate them like this:
1. Yellow triangle on the bottom
2. Blue square on top of the triangle
3. Red circle on top of the square
This is also an example of a monoid action because you used a set of rules (the monoid) to perform an action (rotating the blocks) in a certain way.
In short, a monoid action is simply using a set of rules (the monoid) to perform tasks or actions on a set of objects (in this case, blocks).
A monoid is like a set of rules on how you can play with these blocks. For example, you could have a rule that says you can only stack the blocks in a certain order.
An action is when you actually play with the blocks using these rules. So let's say you have three blocks: a red circle, a blue square, and a yellow triangle.
If your monoid rule is to stack the blocks in alphabetical order of their shape names, you could stack them like this:
1. Yellow triangle on the bottom
2. Red circle on top of the triangle
3. Blue square on top of the circle
This is an example of a monoid action because you used a set of rules (the monoid) to perform an action (stacking the blocks) in a certain way.
Another example of a monoid action could be rotating the blocks. Let's say you have the same three blocks, but this time your monoid rule is to rotate the blocks in order of their colors.
You could rotate them like this:
1. Yellow triangle on the bottom
2. Blue square on top of the triangle
3. Red circle on top of the square
This is also an example of a monoid action because you used a set of rules (the monoid) to perform an action (rotating the blocks) in a certain way.
In short, a monoid action is simply using a set of rules (the monoid) to perform tasks or actions on a set of objects (in this case, blocks).