I should have been more careful. I forgot that when the North Side market was opened in 1863, it was in the city of Allegheny, which was annexed to Pittsburgh in 1907. The market was located on what was called Diamond Square. The caption is correct.

Based on old maps, street views, and other online photos, I'm pretty sure this market was located where the Three Allegheny Center is now, with what is now the restored 1890 Museum Lab of the Children's Museum of Pittsburgh in the background.
https://www.post-gazette.com/news/science/2019/04/04/Museum-Lab-Children...
South Diamond ran along the line of Allegheny Square East.

While the street sign does indeed indicate "S DIAMOND ST E", the one that is now Forbes Avenue at Market Square wasn't the only Diamond Street in Pittsburgh.

This 1920 map shows N, S, E and W Diamond Streets surrounding the intersection of Federal and Ohio in Allegheny Center. And that's definitely the Carnegie Free Library of Allegheny building in the background.

The market would be located on the south side of the Carnegie building, now occupied by an apartment building called 3 Allegheny Center.

My attention is drawn to the two women at far right. They're both focused on something off camera and appear to be inspecting it closely. Whatever it is, it does not interest any of the men. I'm guessing they're disapproving some woman's hat which does not meet the lofty meringue standards of their own millinery creations.

Penny on the tracks!

The car on the far left has right hand drive. The changeover to left hand drive came in 1909.

[It didn't come in any particular year. Cars of the era were a mix of right- and left-hand-drive. Even in 1920 there were still some American cars being built with RHD. - Dave]

From some guy named Prada.

I'm amused at these early 20th Century photos that always feature "Oysters" on a food menu. You rarely see them on a menu today. Frankly, I think they're kind of, well, yucky, for want of a better word.

There’s a renewed interest in resurrecting the city identity of Allegheny 100 so years after it was absorbed into Pittsburgh proper. www.alleghenycity.org

This is not the Diamond Market. It's the North Side Market House at the corner of Federal and Ohio Streets on Pittsburgh's North Side. Here's another view of it: https://historicpittsburgh.org/islandora/object/pitt%3A715.148222.CP. The clock tower behind the market is part of the original North Side Carnegie Library building. The Diamond Market was a very different building in downtown Pittsburgh on what used to be Diamond Street, now Forbes Avenue. Here's some information about it: https://historicpittsburgh.org/islandora/object/pitt%3A1998.52.1/viewer. Federal Street is wide and Diamond/Forbes is narrow. The trolley tracks passed through the Diamond Market. Both buildings and the trolleys are long gone. Market Square occupies the space where the Diamond Market was located. I remember shopping in both of them with my mother when I was very young. Sawdust was liberally sprinkled on the floor of the North Side Market.

[The street sign on the building says South Diamond Street East. - Dave]

Baskets. But where does one find tiskets and taskets, to go with?

I have heard that Market Square has been spruced up since I left Pittsburgh about ten years ago. I hope that's true, as it had the potential to be a great public space.