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Rename wild higher categories #1233

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@fredrik-bakke fredrik-bakke commented Jan 4, 2025

This PR renames "noncoherent wild higher categories" to "noncoherent ω-categories". The latter is both shorter and more descriptive. Additionally, this PR renames "isomorphisms in ω-categories" to "coinductive isomorphisms in ω-categories", as the concept that was defined is strictly weaker than the proper definition of an isomorphism in an ω-category, as discussed with @VojtechStep.

Co-authored-by: VojtechStep [email protected]

@fredrik-bakke fredrik-bakke marked this pull request as ready for review January 7, 2025 15:55
@fredrik-bakke fredrik-bakke changed the title Renaming wild higher categories Rename wild higher categories Jan 7, 2025
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What is the precise proposal for the use of the word "noncoherent"? Is it for omega-categories without any laws at all?

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fredrik-bakke commented Jan 7, 2025

What is the precise proposal for the use of the word "noncoherent"? Is it for omega-categories without any laws at all?

It's meant for any sort of (pre-)category without any laws at all. If it has one level of coherence I'm thinking to call it 1-Coherent-(ω-)?Category. I'm less sure what to call (∞,n)-categories or truncated categories.

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