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created a stub for no-cloning theorem.
For the moment what I wanted to highlight is that under the identification of linear logic as quantum logic it is this theorem which is the “linearity” of the logic.
one more in the list of quantum programming languages
brief category:people
-entry for hyperlinking references at non-abelian T-duality and elsewhere
fixed the pointer to:
I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to
added some references on constructive analysis here.
stub for Goodwillie calculus
edit publication data for:
stub for totalization
I added some material to Peano arithmetic and Robinson arithmetic. At the latter, I replaced the word “fragment” (which sounds off to my ears – actually Wikipedia talks about thisterm a little) with “weakening”.
Still some links to be inserted.
Added to Dedekind cut a short remark on the -stability of membership in the lower resp. the upper set of a Dedekind cut.
conformal block and Vassily Gorbounov. Update at Imma Galvez.
created Stokes theorem
I have added references to two (overlapping) papers which list elementary examples of factorization systems associated with the notions of: compact, discrete, connected, and totally disconnected spaces, dense image, induced topology, and separation axioms; finite groups being nilpotent, solvable, torsion-free, p-groups, and prime-to-p groups; injective and projective modules; injective, surjective, and split homomorphisms.
Anonymous
I have added to orthogonal factorization system
in the Definition-section three equivalent explicit formulations of the definition;
in the Properties-section the statement of the cancellability property.
Wanted to add more (and to add the proofs). But have to quit now. Maybe later.
I have been polishing and expanding the entry weak factorization system:
gave it an Idea-section;
gave the definitions numbered environments and full details;
spelled out the proof of the closure properties in full detail.
Regarding notation: I decided to use as generic name for a weak factorization system:
not , as used to be used in the entry (for that’s already my preferred generic choice for pairs of adjoint functors on the Lab, and for discussion of Quillen adjunctions the notation conventions would clash);
not or the like, since that gives no hint as to what is meant (running into an “” in the middle of some discussion, the reader is always at risk of having to browse back to figure out which class is meant);
but… , for that is nicely indicating what is meant.
I started reworking a quasi-periodic study of mine on propositions as types that introduces the factors of "proof hints" and "untyped terms" into the analogy.
Update . This material is now at propositions as types in combinatory algebra.
After discussion here I have changed the organization of the entry structure and then expanded a bit by adding an Idea-section and a bit more here and there.
(The previous organization of the entry instead made it look like structure in model theory is a concept on par with that discussed at stuff, structure, property. But instead, the latter axiomatizes the general notion of “structure on something” as such, whereas the former is an example of a structure on something (namely an “-structure on a set”). The new version aims to reflect this properly.)
a bare list of references, to be !include
-ed into the References-sections of relevant entries (such as at qbit, quantum computation, nuclear magnetic resonance), for ease of synchronizing
added at adjoint functor
more details in the section In terms of universal arrows;
a bit in the section Examples
I finally wrote this: intuitionistic mathematics.
Included the condition on sequential (co)limits that the indexing ordinal should be nonzero, which I presume to be the correct convention. (e.g. based on the description they are a special case of filtered colimits)
I keep feeling the need to point to an entry named formal logic. None of the existing entries seems to quite deserve to be where this link should be redirecting to. So I created a page formal logic with just some pointers to pages that the reader might expect behind this term.
Just so that I can use that link for the time being.
I have added the Tarski reference to intuitionistic logic and internal logic
!include
-ed the logic symbols – table into this old stub entry
created Whitehead theorem, including its (oo,1)-topos version
in that context I also created hypercomplete (infinity,1)-topos. maybe that should be merged eventually with hypercompletion.