Minor comments and corrections

[falsifian]

Hi Adele,

Thanks for pointing me this writeup last month. I noticed a few minor errors or places for minor improvements; sending along in case they're helpful.

I'm reading the pdf from this repositor which it looks like you compiled on July 31.

Notes:

• p. 5, below Definition 4: "Forget(f) to Forget(f)" should probably be "Forget(R) to Forget(R)", and same for "lambda in Forget(f)" later in the paragraph.

• p. 7: "for each morphisms": should be "morphism"

• p. 8: I found it a bit confusing that d_i is used to denote two different kinds of thing:

  -> d_i is used to denote a formal map from a particular (n+1)-simplex to a particular n-simplex. E.g. in this text: "the face maps are morphisms in the opposite category". With this usage, one simplicial complex has several morphisms called d_0, and the domain and co-domain of each d_0 are simplices.

  -> d_i also denotes a function where the domain and range are the set of simplices in the complex. For example, the relation d_i dj = d{j-1} d_i (just before Definition 12) seems to be using this interpretation. With this interpretation, a simplicial complex has one function d_0, and if A is an (n+1)-simplex, then d_0(A) is an n-simplex.

• Just above section 4.2: "f : [2] -> [1] mapping 0 -> 0, 1 -> 1 and 2 -> 2" --- the domain and range can't be [2] and [1] here, e.g. 2 is in the range.

• James

[falsifian]

@adelejackson

[adelejackson]

Thanks for this! I haven't had time to go over these corrections, but just wanted to say I appreciate them and will use them.

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