It's a lot of machinery to make precise, but look for basic videos for a taste. This is aight (looked for a few, but nothing short and good covers it well afaict),
https://youtu.be/sgzPex6FIbA
Doesn't cover the homology thing, but complexes is covered quickly. He has subsequent videos that go deeper, but this much is cool to learn about, if no other reason than knowing it's the mathematically precise way to frame the subject sheds a lot of insight imo
