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Stub context-free grammar.
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category: people page for reference
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Added more material to Boolean algebra, particularly the principle of duality and the connection to Boolean rings, and a wee bit of material on Stone duality.
Stone duality deserves greater expansion, bringing out the dualities via ambimorphic (ahem, schizophrenic) structures on the 2-element set, and mentioning the connection to Chu spaces. Another day, another dollar.
I’ve inserted proofs of equivalence of the three conditions listed in the definition of De Morgan algebra.
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Made some further tweaks at cubical set. Hopefully the definitions of the boundary functor, and of a horn, are correct now.
Am continuing to work on homotopy groups of a cubical Kan complex.
Adding reference
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category: people page for reference
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category: people page for reference
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category: people page for reference
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category: people page for reference
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category: people page for references
{#CF77} William H Cornish, Peter R Fowler, Coproducts of de morgan algebras, Bulletin of the Australian Mathematical Society, 16(01):1–13, 1977. (pdf)
{#CF79} William H Cornish, Peter R Fowler, Coproducts of kleene algebras, Journal of the Australian Mathematical Society (Series A), 27(02):209–220, 1979
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category: people page for references
{#CF77} William H Cornish, Peter R Fowler, Coproducts of de morgan algebras, Bulletin of the Australian Mathematical Society, 16(01):1–13, 1977. (pdf)
{#CF79} William H Cornish, Peter R Fowler, Coproducts of kleene algebras, Journal of the Australian Mathematical Society (Series A), 27(02):209–220, 1979
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Adding reference
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added statement of existence of linear extensions (here)
Will give this its own entry at linear extension of a partial order, for ease of referencing
moving material about composites of morphisms from composable morphism into its own page
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splitting this off from su(2)-anyons: Copied much of the material over, but also added a few more sentences.
For the moment this entry is a cautionary tale about confirmation bias more than an entry about physics.
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I finally created an entry internal category in homotopy type theory.
There is old discussion of this topic which I had once written at category object in an (infinity,1)-category in the sub-section HoTT formulation, but it’s probably good to give this a stand-alone entry, for ease of linking (such as from equivalence of categories now).
It was pointed out to me today that in the very special case of internal (0,1)-category objects in Set, what we are calling a “pre-category” reduces to a preordered set, while adding the “univalence/Rezk-completeness” condition to make it a “category” promotes it to a partially ordered set. I feel like surely I knew that once, but if so, I had forgotten. It provides some extra weight behind this term “precategory”, especially since some category theorists like to say merely “ordered set” to mean “partially ordered set”.
added to complete Segal space a discussion of what an ordinary category looks like when regarded as a complete Segal space.
(This is meant to be pedagogical, therefore the recollection of all the basics at the beginning.)
added pointer to:
added to groupoid a section on the description in terms of 2-coskeletal Kan complexes.