The outgoing president and vice president normally attend the inauguration of their successors. This is so automatic that, according to the inauguration committee, no invitation is sent because none is needed. Any arrangements are made at the staff level.

But now CNN is reporting that Pence wants to attend the Biden/Harris inauguration, and he wants an invitation to do so.

Pence planning to attend Biden inauguration but awaiting invitation, source says

Vice President Mike Pence is planning to attend the inauguration of Joe Biden but is waiting on an invitation, a source close to him confirmed to CNN on Thursday.
“That’s the plan,” the source said.

But. . .

“You can’t attend something you haven’t received an invitation to….” Devin O’Malley, Pence’s deputy press secretary tweeted after Politico first broke the news of the vice president’s plan.

Politico thinks Pence’s decision was triggered by Trump criticizing (to put it mildly) Pence’s insistence on following the law and the Constitution:

Three sources close to Pence said he would likely make an appearance at the Jan. 20 event in a show of support for the peaceful transition of power. The decision to attend, they said, became easier after President Donald Trump publicly criticized Pence leading up to, and following, his refusal to stop the certification.

But I would say Trump’s behavior yesterday was another straw added to a broken camel’s back. From the CNN story:

Pence’s decision to attend marks another major break between Pence and Trump, who publicly attacked the Vice President on Wednesday as Pence prepared to certify the election results.
Trump did not call to check on Pence’s wellbeing even as an angry mob roamed the halls of the Capitol shouting about Pence, and even after the vice president was evacuated from the House floor.

So. On the one hand, inviting Pence to attend the inaugural would be the sort of gesture Biden is inclined to make, “healing the country” and so on. Plus it acknowledges that Pence did refuse to take part in or aid-and-abet Trump’s attempts to steal the election. Also, if Pence ever had any thought of getting the Republican nomination in 2024, he has to know he lost that when he crossed Trump once, just once. So there is no political downside for him to do the usual and honorable thing.

On the other hand, Pence spent the past four years aiding and abetting Trump, gazing adoringly at him in a way that would have made Nancy Reagan blush. Plus there’s all the things Pence did as Indiana governor.

Most significant, Pence has yet to meet with Kamala Harris, his successor, the way Biden met with Pence in 2016.

It would be a courtesy to extend an invitation to Pence (and not to send one to Trump, reinforcing the contempt everyone holds for him). But I would make it clear that Pence will get that invitation only after he does the courteous thing and meets Harris.

(I have a feeling he wants to do that anyway, and that Trump ordered him not to. Just as he ordered Pence not to attend the inauguration.)