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Currently, the description is

Algebraic topology is a mathematical concept that uses algebraic tools to study topological spaces. In other words, it is the intrinsic qualitative aspects of invariant spatial objects under homeomorphic transformations.

I don't think I like this, it sounds too soft.

I would suggest rewriting it as

Algebraic topology is a mathematical subject that uses algebraic objects associated to topological spaces that are invariant under homeomorphism or homotopy equivalence. We often require that these associations are functorial so that continuous maps induce morphisms of some algebraic object.

I know this is somewhat crude, and maybe overly technical, but I would be happy to see what the community might suggest for a rewrite (or even if others think the current desciption is okay.)

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    $\begingroup$ As you have mentioned yourself, I think for someone who had no contact to algebraic topology so far, your rewrite might be shocking. So better keep it simple? $\endgroup$ – Cornman May 11 at 3:45
  • $\begingroup$ @Cornman do you have a specific suggestion? I'm glad to simplify it but I can't tell exactly where I should do that. $\endgroup$ – Andres Mejia May 11 at 16:07
  • $\begingroup$ Unfortunatly not, but after the answer of Eric Wofsey it seems, that it does not matter that much. $\endgroup$ – Cornman May 11 at 21:07
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I would change "We often require that..." to simply "Often" but otherwise this looks like an improvement to me. Certainly the current phrase "intrinsic qualitative aspects of invariant spatial objects under homeomorphic transformations" is terrible.

For what it's worth, tag wikis are not very important--they are obscure, hard to find, and not read often (the tag wiki currently has only been viewed 414 times in about 4 years). This is in contrast with the excerpts which appear when mousing over the tag, which are seen every time someone selects a tag for their question and are important for providing guidance on when to use the tag. So, I would recommend being bold and not hesitating to just make edits like this to tag wikis without asking here on meta first. At your current reputation level any edits you make will be reviewed anyways, so there is some oversight in case you're doing something terribly wrong.

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