this is a pretty discussion but not a very good one if you don't already know some things. for example >the holes of dimension 0 are unconnected components i

this is a pretty discussion but not a very good one if you don't already know some things. for example >the holes of dimension 0 are unconnected components in this sentence >the holes of dimension 0 are unconnected components, the holes of dimension 1 may be surrounded by a loop, whereas those of dimension 2 may be enclosed by surfaces stands out because it's the only classification that's formal (i actually don't know what the meaning of unconnected component here is but i suspect it means a point?). then C(X) is defined informally as >The set of "objects of dimension 𝑘" will be denoted 𝐶𝑘(𝑋) but this informal definition doesn't say explicitly that it's the set of objects in X (until later). then orientation is defined in a very confusing way >for now it will be some additional property that takes two opposite values ("one the negative of the other one") but i will say that the discussion of quotienting was kind of an aha moment for me (about why you'd rather work in the quotient than the set itself) and i've been dipping toes into algebra for a loooooong time. anyway you kind of have to read it like a poem (in that you should try to get a feeling rather than a precise idea) but that's not very useful. also i'm interested in how the diagrams were created. looks like latex + tikz? also it would've make more sense to show >im ∂𝑘⊂ker ∂𝑘-1 instead of >im ∂𝑘+1⊂ker ∂𝑘 to stay with the notation in the previous sentence