There is a word I read some years ago, which was used in a philosophical context to express the idea of people having the same concept or understanding of something. It might have been discussed in the context of semiotics or epistemology, I can't remember exactly.
The idea in that context was: how do we check that we all have the same understanding of X concept or thing. And this word - which may start with the prefix "con-" - designated that specific reality of people having a shared understanding of something. Its connotations implied commensurability and commonality in terms of cognition.
I have one of those "word being on the tip of your tongue" moments, but I can't contextualise this word enough that I could find it by searching it somewhere. It might be a very specialised word, that is only used in very specific contexts where philosophical, semiotic or even scientific methodology is discussed. I think I first heard this word at a university course, that's why I'm thinking it might be related to one of those fields.