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Why is this checkmate?

I played this chess puzzle offline: lichess.org/training/1542

The puzzle results in checkmate with the Queen (protected by the Bishop on G7) attacking the King on A1. However, the Bishop is pinned by the white Queen, therefore the Bishop cannot protect any pieces. Therefore, the white King could capture the black Queen, and there is nothing black could do about it. All things considered, the black Queen should be considered sacrificed.

I am confused as to why pinned pieces are not taken into consideration when it comes to checkmate. Is this actually a legal mate?
Yes, the way I think about it is that if you can capture the opponents king first then you automatically win even if you put yourself in danger. Since if theoretically the king did take the queen it could be immediately captured next move. You could also think about it as all of your opponents pieces becoming immobilized if you capture their king.
@EugeneJudo

Let's say I moved my Queen along the diagonal of my Bishop to a place where white could capture it. In that case, I couldn't take back with my Bishop, and my Queen would be gone. Why doesn't the same thing apply to the King? He could just take it back and black would be helpless.
It is correct. If you were not aware of it before, you can learn it from this puzzle: A piece pinned like the black bishop in this position cannot move, but it d o e s certainly keep his influence over the board. The mate on b2 is legal and the king cannot capture it.
That is just the way it is, but it is good that you noticed it and can use this knowledge in the future.
Thank you all for the replies!

I just don't like it: pinned pieces should not be considered active when attempting check or checkmate. In my opinion, they are considered, for lack of a better term, "dead weight" until the pin is removed. I don't see why attacking the King should be an exception.
Well, it is up to you to learn how it is or to have an opinion. Maybe your opinion will come closer to the spirit of the rules the more familiar you get with the game.
#3, consider that if the king did capture the queen then you could capture the king immediately. Putting yourself in this kind of position is against the rules regardless whether or not the piece defending that square is itself pinned. Imagine that if you capture your opponents king that all of their pieces disappear, then no pin would exist allowing you to capture with the bishop (the game ends one move before this since checkmate).
Just to mention it: Not only can the queen on b2 not be captured. Of course the W king cannot enter any square that is controlled by the pinned bishop on g7.
Where it different you might just imagine a W king marching up the board on the diagonal via b2, c3, d4, e5, f6 and it would all be fine!? I think this absurd example makes it pretty clear that the pinned piece does not and also should not lose its influence over the board.
My reasoning for why that example *would* be all fine is if, say, the black King moved out of the pin, then that is a new way to have a discovered check against the white King, and thus causing white to either capture the black Bishop, block the attack, or move the King. I think it would be an interesting addition to the chess rules, though I suppose I'll accept the rules as they are and move on.
The king cannot move to a square controlled by an enemy piece. If the piece is pinned or not is irrelevant to that rule.

The bishop is controlling a1, therefore the king cannot go to a1.

There is not such thing as capturing a king in chess. The game always ends just before that.

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