“Albert is asking us to notify him of any revisions we make to the extensions sheet.”
A coworker from another department in your company has complained because people on your team don't tell him about changes that you've made to a document that is shared between your groups. You're explaining to another team member that he wants you to tell him about new changes.
Albert is asking us to notify him of any revisions we make to the extensions sheet.
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(someone) is asking (someone) to (do something)
In the example above, the speaker uses "is asking" instead of "asked". You can use "is asking" to talk about a question that someone has asked, but you haven't given an answer to yet. In the example above, Albert has asked for notifications whenever your team makes revisions to a document. But your team hasn't decided if it will agree to do that yet. So part of the meaning of the sentence above is "Albert is asking us to do this, but I'm not sure if we should agree to do it."
notify (someone) of (something)
To "notify" someone of something just means to tell them. You "notify" people of things that are new and that the person might need to know or might find interesting.
The word "notify" is more formal than just "tell" and is often used in business situations. Here's another example. When writing an e-mail to a client, you can offer to help when they have problems by saying:
Please notify me of any problems or questions that come up.
make revisions to (a document)
A "revision" is a change that you make to a document that has already been finished or published. To "make revisions to ___" means to change part of something.
You can also use the verb "revise" instead of "make revisions". In the example at top, that would make the sentence:
Albert is asking us to notify him whenever we revise the extensions sheet.
There's not a really strong difference between this version and the original version. But I think the original version sounds just a little more natural.
An "extension" is extra time that someone gives you after a deadline to finish something. So the "extensions sheet" is probably a document where people record when things can be finished that are going to go past the usual deadline.
a (something) sheet
In an office environment, a spreadsheet or document can be called a "___ sheet". You can make up a name for a document that you've written and shared with coworkers. Some examples include:
the daily expenses sheet
a committee sign-up sheet