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following public demand, I added to tensor product of chain complexes a detailed elementary discussion of the tensor product of the (normalized) chain interval with itself, and how it gives chains on the cellular square: in Square as tensor product of interval with itself.
expanded the Idea-section and added a reference:
added the examples of differential graded-commutative algebras and of differential graded-commutative superalgebras
stub for complex structure
wrote a sentence at complexification
stub for homotopy type theory
created an entry modal type theory; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with monad (in computer science).
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:
A survey of various notions between unital rings and nonunital rings:
added publication details for this reference:
and am copying it over to compactly generated topological space, too
creating a minimum entry, to satisfy long-requested links in entries such as permutation group heap
The cut rule for linear logic used to be stated as
If and , then .
I don’t think this is general enough, so I corrected it to
If and , then .
I started a stub at affine logic as I saw the link requested in a couple of places.
mostly to collect some references, prodded by today’s review:
a bare minimum, for the moment just to make links work (such as at probability amplitude and at Wigner’s theorem)
The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.
created (finally) lax monoidal functor (redirecting monoidal functor to that) and strong monoidal functor.
Hope I got the relation to 2-functors right. I remember there was some subtlety to be aware of, but I forget which one. I could look it up, but I guess you can easily tell me.
We had a stub at symmetric monoidal natural transformation but not at monoidal natural transformation, so I put one there.
Following discussion in some other threads, I thought one should make it explicit and so I created an entry
Currently this contains some (hopefully) evident remarks of what “dependent linear type theory” reasonably should be at least, namely a hyperdoctrine with values in linear type theories.
The entry keeps saying “should”. I’d ask readers to please either point to previous proposals for what “linear dependent type theory” is/should be, or criticise or else further expand/refine what hopefully are the obvious definitions.
This is hopefully uncontroversial and should be regarded an obvious triviality. But it seems it might be one of those hidden trivialities which deserve to be highlighted a bit more. I am getting the impression that there is a big story hiding here.
Thanks for whatever input you might have.
Finally created funny tensor product. This is not really a very good name for a serious mathematical concept, but I don’t know of a better one.
New page at sesquicategory.
Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).
added to the Properties-section at Hopf algebra a brief remark on their interpretation as 3-vector spaces.
added these references, and added their doi etc.:
Early speculations trying to model the electron by a relativistic membrane:
{#Dirac62} Paul Dirac, An Extensible Model of the Electron, Proc. Roy. Soc. A268, (1962) 57-67 (jstor:2414316)
Paul Dirac, The motion of an Extended Particle in the Gravitational Field, in Relativistic Theories of Gravitation, Proceedings of a Conference held in Warsaw and Jablonna, July 1962, ed. L. Infeld, P. W. N. Publishers, 1964, Warsaw, 163-171; discussion 171-175 (spire:1623740)
Paul Dirac, Particles of Finite Size in the Gravitational Field, Proc. Roy. Soc. A270, (1962) 354-356 (doi:10.1098/rspa.1962.0228)
I rewrote the few sentences at tangent (infinity,1)-category in an attempt to make it run more smoothly.
In any case, there is not much there yet...
created a currently fairly empty entry quantum measurement, just so as to have a place where to give a commented pointer to the article
I made some edits at well-order. I am removing a query box, having duly extracted some punchlines. These edits also forced an edit to partial function, where I added the generalization to partial maps in any category with pullbacks.
+– {: .query} This need not exist; in particular, may be empty. What do we really want to say here? (We could talk about the successor of a well-ordered set.) —Toby Mike: Yeah, or we could say that successor is a partial function. One definition of a limit ordinal is one on which successor is totally defined. =–
Added a bit to Hartogs number. Including the curiosity that GCH implies AC. :-)
I have made explicit the example of involutive Hopf algebras, and how most of the other examples previously listed here are special cases of this one. Also expanded a little and organized it all into a new Examples-subsection (here)
slightly edited AT category to make the definition/lemma/proposition-numbering and cross-referencing to them come out.
Probably Todd should have a look over it to see if he agrees.
it has annoyed me for a long time that bilinear form did not exist. Now it does. But not much there yet.
started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective