Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of βcontinuation-passingβ transform.
Iβve 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 C, and form a new 2-category with 2-products Mon(C) whose 0-cells are pseudomonoids in C, 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 Mon(β), starting with C=Cat. Why isnβt this the βrightβ notion of iterated monoidal category, or in other words, why do Balteanu, Fiedorowicz, SchwΓ€nzel, and Vogt in essence replace Mon(β) with Monnorm(β) (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, β¦ 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 G2 as the subgroup of GL(7) 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.
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.
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
We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.
Move to clopen subset (since it's a relative notion, agreeing with open subset and closed subsetl
More examples added at principal ideal domain.