Two final points. First I am using "concept" here as a shorthand for concept-mediated practices, where the reality is always the practice-in-activity. Concepts as some sort of non-material realities in themselves make no sense to me. And second, there is an asymmetry in the relation of concept and institution. You can't, I think, define a concept apart from its grounding institution and the activities and practices normal to that institution. But you could not I think successfully define an institution through its associated concepts (though some people do try to do this, for example, with Mathematics, and even far less plausibly with the natural sciences).
But to end by crossing two recent threads: if concepts are embedded in institutions, and concept learning is part of a development that always depends on affects, should we expect that institutions not only have their characteristic concepts, but also their characteristic emotional feelings? And that learning an institution-grounded concept therefore also means learning to feel emotionally in the "style" of that institution?