At the Daily Show’s Donald J Trump Presidential Twitter Library there are no books, for reasons that don’t require explanation. But there are tweets – lots of them.

Conceived of and curated by the Daily Show team, the pop-up museum just around the corner from Trump Tower is arranged like the libraries of presidents past, memorializing Trump’s tweets from 2009 onwards.

His greatest hits (“covfefe,” for instance) appear in gilded frames aside context-providing placards, while other tweets are bracketed by category, pop culture reflections in one corner, admonishments of political rivals and heads of state in another.

“Shouldn’t the presidential library be at the end of a president’s term?” Daily Show host Trevor Noah asked reporters in a makeshift Oval Office adorned with a golden toilet and chenille bathrobe (the letters “DT” emblazoned on the chest).

“Yes, that’s true. Unfortunately, we do not know when his term will end. It could be next week, it could be never. So we decided to do it now,” he added.

Trevor Noah. Photograph: Getty Images for Comedy Central

The project is a sort of snark-laden salute to a president who communicates primarily in 140-character aspersions, an undiluted look into his many grievances. “He may not be good at president-ing, or leading, or geopolitics, but he is a damn fine Twitterer,” Noah added.

The end result is a fascinating trip through the annals of his convoluted conscience, a satire that’s equal parts jarring and funny, absurd and “Sad!”.

He may not be good at president-ing, or leading, or geopolitics, but he is a damn fine Twitterer Trevor Noah

Upon entry, you first encounter the president’s notorious Cinco de Mayo tweet (“I love Hispanics!” he wrote, before hailing the taco bowls at Trump Tower Grill), an exercise in how one “panders to minorities while also plugging your businesses”, as comedian Hasan Minhaj joked at a press preview.

He went on: “Sometimes, when a person drops a new album, the blogosphere goes crazy about it, but don’t forget his early mixtapes. People sleep on the early Cinco de Mayo tweet.”

The exhibit goes on to chronicle Trump’s many feuds, from “the Bushkrieg”, a series of tweets lambasting Jeb Bush (“just watched Jeb’s ad where he desperately needed mommy to help him,” one reads), to Trump’s late 2012 polemic against soda pop. “I have never seen a thin person drinking Diet Coke,” he wrote, curiously.

In a section called Trump v Trump, a screen shuffles through past tweets in which the president holds diametrically opposed positions, explaining that while “most politicians base their decisions on strongly held beliefs, Trump’s brain is so uniquely good (or great) that it can hold many different beliefs on the same subject”.

The Donald J Trump Presidential Twitter Library. Photograph: Getty Images for Comedy Central

“The electoral college is a disaster for democracy,” Trump wrote on 6 November 2012. Almost four years to the day later, after his own electoral college victory, he praised the system: “The electoral college is actually genius in that it brings all states, including smaller ones, into play.” Next up is a convenient bait-and-switch on Syria, the president having gone from anti-interventionist grandstander to trigger-happy neocon.

Inside the library is a live feed of Trump’s account, with sirens wailing loudly each time he posts something new. There’s also a monitor quantifying his Twitter habits, like the frequency with which he mentions different family members (daughter Ivanka clocks in at over 500, daughter Tiffany at seven) and attacks political nemeses (Barack Obama has, astoundingly, fielded more than 2,700 Trump Twitter tirades).

“It’s about giving context to the tweets,” Trevor Noah said. “Not absorbing them one bite at a time, but rather looking at them as a body of work.”

When asked if Trump-centric comedy was being exhausted, Noah rejected the idea outright. But with a one-man joke generator in the White House, comedians’ attempts to mock the president have been generally met with either short-lived viral status or, in Kathy Griffin’s case, job loss.

The Daily Show’s exhibit, though, is perhaps the best skewering of Trump yet, mainly because it takes the tweets he’s so proud of and uses them as a springboard to exhibit his bluster and blasphemy.

It’s easy to willfully forget that the president once tweeted a message to “the haters and losers” on “this special day, September 11th”. Or that he took particular umbrage at Modern Family writer Danny Zuker, who he said had “the mind of a very dumb and backward child”. Or that he peddled his racist birtherism conspiracy for longer than I’d initially realized. Or that he once tweeted, simply, “We”.

But the Donald J. Trump Presidential Twitter Library doesn’t let you and, in that sense, it’s a sort of brick-and-mortar tribute to every American who considers the president a national embarrassment, a moral and intellectual outrage.

That it stands just a stone’s throw from Trump Tower is the cherry on top.