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fix: proofread Category Theory part - #333

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fix: proofread Category Theory part#333
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@vEnhance vEnhance commented Jul 6, 2026

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Proofreads the Category Theory part (issue #315), covering the chapters tex/cats/categories.tex, tex/cats/functors.tex, tex/cats/limits.tex, and tex/cats/abelian.tex.

Most fixes are minor typos and grammar. A couple are small notation/logic slips worth calling out:

Notation / correctness

  • functors.tex — In the covariant Yoneda functor example, the action on arrows was written as H_A(f) (subscript, the contravariant Yoneda functor) instead of H^A(f) (superscript), which is the functor actually being defined there.
  • abelian.tex, four lemma solution — When lifting a' to a ∈ A with α(a) = a', the justification read "Since α is injective"; existence of such an a uses that α is surjective (epic), which is what the hypothesis actually provides. Fixed the word.
  • abelian.tex, short five lemma proof — The symbol c' was used before being defined; now set c' ≔ q'(b') explicitly. Also fixed a stray β' (no such map in the diagram) to β.

Typos / grammar

  • categories.tex: "one-Object" → "one-object"; "I can use it build" → "use it to build".
  • functors.tex: "the first slots" → "the first slot"; "an object of B" → "an object B"; "specify Set-map" → "specify a Set-map"; "viewing functor" → "viewing a functor"; "because, ... then" → "because, ... we have"; "that do what we want" → "that does".
  • limits.tex: "give a you taste" → "give you a taste"; "homorphism" → "homomorphism"; "pairs of errors" → "pairs of arrows".
  • abelian.tex: "the most natural things ever" → "thing"; added a missing period.

No large mathematical errors were found; the arguments in these chapters check out.

🤖 Generated with Claude Code

https://claude.ai/code/session_01NgyfoveJybAdVwGSWvYEww


Generated by Claude Code

Fix typos, grammar, and notation errors in the Category Theory
chapters (tex/cats/*.tex):

- categories.tex: "one-Object" -> "one-object"; add missing "to" in
  "use it to build".
- functors.tex: correct covariant Yoneda functor notation from
  H_A(f) to H^A(f); fix several article/grammar typos.
- limits.tex: "give a you taste" -> "give you a taste"; "homorphism"
  -> "homomorphism"; "pairs of errors" -> "pairs of arrows".
- abelian.tex: define c' in the short five lemma proof; fix "beta'"
  -> "beta"; correct the four lemma solution to invoke that alpha is
  surjective (epic), not injective, when lifting a'.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NgyfoveJybAdVwGSWvYEww
@vEnhance vEnhance added the proofreading-campaign Systematic full proofreading of text label Jul 6, 2026 — with Claude
@vEnhance vEnhance mentioned this pull request Jul 6, 2026
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vEnhance merged commit d5b3a4d into main Jul 9, 2026
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