[gnulinux]

Monads are algebraic objects that conform to certain axioms. The same way burritos and elephants can end up being groups, rings, Hilbert spaces or whatever under right conditions and right operations, many things can be monad too, under the right operation. The issue with these monad tutorials are in their very premise. They want to explain what monad is without giving its mathematical definition (and its mathematical context) but this inevitably causes significant amount of nuance to be lost.

[nerdponx]

A "mathematical object" in this case is a description of how the object is expected to behave.

But even so, I think something is lost in reducing monads to a clump of related behaviors and properties. You still need intuition about what these behaviors actually mean and what kinds of real-world objects actually conform to these properties.

So you are right that monad "is not" a nondeterministic computation or a container or whatever, but a monad "is" a common set of behaviors/properties that we should expect nondeterministic computations and containers to conform to.

Abstraction without intuition is obfuscation!