Just realised I may have missed your point; anyway, you're right that "monoid" is harder to find an easily-understood counterpart for than "container". There ar

Just realised I may have missed your point; anyway, you're right that "monoid" is harder to find an easily-understood counterpart for than "container". There are examples of monoids which everyone is probably familiar with, but we don't usually abstract from those everyday examples; whereas as well as there being everyday examples of containers (boxes, bags), we are familiar with abstracting away from those examples in everyday life to come up with the general concept of container.