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What is a good notation for the set'set' (or stack if you insist) of all principal G bundles over all'all' spaces for given G? BG is way over used. How about Bun(G)?
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The `set' of all principal G bundles over `all' spaces

What is a good notation for the set' (or stack if you insist) of all principal G bundles overall' spaces for given G? BG is way over used. How about Bun(G)?