The very much down-market rival of the Ankh-Morpork Times.
It was created by Ronald Carney, the long-time admirer of Sacharissa Cripslock. His reasons were manifold, but principally because he worked as an Engraver, and the Engravers were enraged by the idea of movable type in Ankh-Morpork. As the Times was using it, and setting engravers out of work everywhere, there was an emergency meeting of the guild, and some of the younger generation made themselves heard - mainly by pruning some of the dead wood found at the top of every civil body and dragging the guild "kicking and screaming into the Century of the Fruitbat".
In order to best subvert the Times, the Inquirer bought up all the available paper pulp from Harry King, and started selling their product at a ridiculously low price in order to put the Times out of business. The plan being, to finish off this moving type nonsense and either shut it down permanently or - more likely - bring it under the auspices of the guild.
As the Times had something of a monopoly on truth - and long-winded editorials - the Inquirer decided its best course of action would be to sell what people wanted to read, rather than what was actually true or, to put it in William de Worde's colourful language, "Piss in the Fountain of Truth". However, what people want to read is actually quite difficult to write - it's a bit like creating something they want to eat when they are least able to listen to their senses. As such, an ideal candidate stood out as their lead writer...
Following the fire at the Times' office, William and the Dwarfs, under the leadership of Gunilla Goodmountain, "persuade" Mr Carney to lend them what they need to continue publishing, although they do offer the sweetener of at least AM$2000 worth of rubies for the privilege.
As of the events of the later books, the Inquirer is still going but not with Dibbler as a creative input, and is struggling to a profit against a backdrop of an explosion in the printed material now available in Ankh-Morpork, such as Bu-Bubble.
Think of the relationship between broadsheets and tabloids in Britain - on the one hand, the lofty and principled Guardian, and on the other, rather grubby, hand the Daily Star.
In fact, given that in Britain, the Times and the Sun are as opposite as you could ever expect to see, they are both under the same ownership. After events at the end of The Truth, could it be that the Inquirer is likely to be owned by the A-M Times these days?
It does, however, seem that this is a direct reference to The National Enquirer whose stories famously stretch the truth. Allegedly.