fix: proofread Category Theory part - #333
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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
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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, andtex/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 asH_A(f)(subscript, the contravariant Yoneda functor) instead ofH^A(f)(superscript), which is the functor actually being defined there.abelian.tex, four lemma solution — When liftinga'toa ∈ Awithα(a) = a', the justification read "Sinceαis injective"; existence of such anauses thatαis surjective (epic), which is what the hypothesis actually provides. Fixed the word.abelian.tex, short five lemma proof — The symbolc'was used before being defined; now setc' ≔ q'(b')explicitly. Also fixed a strayβ'(no such map in the diagram) toβ.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 ofB" → "an objectB"; "specifySet-map" → "specify aSet-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.
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https://claude.ai/code/session_01NgyfoveJybAdVwGSWvYEww
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