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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
following discussion here I am starting an entry with a bare list of references (sub-sectioned), to be !include-ed into the References sections of relevant entries (mainly at homotopy theory and at algebraic topology) for ease of updating and syncing these lists.
The organization of the subsections and their items here needs work, this is just a start. Let’s work on it.
I’ll just check now that I have all items copied, and then I will !include this entry here into homotopy theory and algebraic topology. It may best be viewed withing these entries, because there – but not here – will there be a table of contents showing the subsections here.
adding references
Ming Ng, Steve Vickers, Point-free Construction of Real Exponentiation, Logical Methods in Computer Science, Volume 18, Issue 3 (August 2, 2022), (doi:10.46298/lmcs-18(3:15)2022, arXiv:2104.00162)
Steve Vickers, The Fundamental Theorem of Calculus point-free, with applications to exponentials and logarithms, (arXiv:2312.05228)
Anonymouse
brief category:people-entry for hyperlinking references at equivariant principal bundle
category: people page for the reference
Anonymouse
category: people page for the reference
Anonymouse
I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of “continuation-passing” transform.
I’ve been inactive here for some months now; I hope this will significantly change soon.
I have written a stubby beginning of iterated monoidal category, with what is admittedly a conjectural definition that aims to be slick. I am curious whether anyone can help me with the following questions:
Is the definition correct (i.e., does it unpack to the usual definition)? If so, is there a good reference for that fact?
Assuming the definition is correct, it hinges on the notion of normal lax homomorphism (between pseudomonoids in a 2-category with 2-products). Why the normality?
In other words (again assuming throughout that the definition is correct), it would seem natural to consider the following type of iteration. Start with any 2-category with 2-products , and form a new 2-category with 2-products whose 0-cells are pseudomonoids in , whose 1-cells are lax homomorphisms (with no normality condition, viz. the condition that the lax constraint connecting the units is an isomorphism), and whose 2-cells are lax transformations between lax homomorphisms. Then iterate , starting with . Why isn’t this the “right” notion of iterated monoidal category, or in other words, why do Balteanu, Fiedorowicz, Schwänzel, and Vogt in essence replace with (where all the units are forced to coincide up to isomorphism)?
Apologies if these are naive questions; I am not very familiar with the literature.
a bare minimum, for the moment just so as to satisfy links from graded modality
I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?
copied over the homotopy-theoretic references from modal type theory to here.
http://ncatlab.org/nlab/show/Isbell+duality
Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here. http://mathoverflow.net/questions/84641/theme-of-isbell-duality
However, this paper http://www.emis.ams.org/journals/TAC/volumes/20/15/20-15.pdf
seems to use another definition. Could someone please clarify?
added to G2 the definition of as the subgroup of that preserves the associative 3-form.
collected some references on the interpretation of the !-modality as the Fock space construction at !-modality.
Cross-linked briefly with he stub entries_Fock space_ and second quantization.
I began to add a definition of conformal field theory using the Wightman resp. Osterwalder-Schrader axiomatic approach. My intention is to define and explain the most common concepts that appear again and again in the physics literature, but are rarely defined, like “primary field” or “operator product expansion”.
(I remember that I asked myself, when I first saw an operator product expansion, if the existence of one is an axiom or a theorem, I don’t remember reading or hearing an answer of that until I looked in the book by Schottenloher).
Added to noetherian ring a homological chacaterization: a ring is Noetherian iff arbitrary direct sums of injective modules are injective.
I have spelled out the proofs that over a paracompact Hausdorff space every vector sub-bundle is a direct summand, and that over a compact Hausdorff space every topological vector bundle is a direct summand of a trivial bundle, here
Added appropriate axioms for the various definitions of affine space, along with another definition in terms of a single quaternary operation.
Unfortunately, there are two entries on the same topic, both created by Urs: quantum Hall effect (redirecting also fractional quantum Hall effect what should eventually split off) with some substance, and the microstub quantum hall effect. I would like to create quantum spin Hall effect and I think I should rename/reclaim the stub quantum hall effect for this. Do others agree ? Urs ?
As the action is now delayed I record here the reference which I wanted to put there
Somewhat surprisingly, the authors and roughly this work of them are mentioned (though not in the list of references) in a paper in algebraic geometry
which considers the mirror symmetry and topological states of matters (topological insulators in particular) as main applications.
created dg-nerve
starting page on right triangles since the paper
talks about right triangles too
Anonymouse
I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here