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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Asked a question at natural transformation.
added pointer to:
removed the following ancient query box discussion:
+–{.query} Left I could understand, but right? —Toby
The way I rewrote it explains it. It is unfortunate that the Eilenberg-Watts theorem treated in Bass was using only right adjoint functors so later they dropped word right. – Zoran
Thanks. —Toby =–
added missing publication data to some references, and added this new reference:
Just discovered that this stub-entry exists, which seems to have been abandoned in the middle of its third sentence.
I have now made minial cosmetic adjustment to the content
and copied over some relevant references from non-perturbative quantum field theory
and I am hereby removing the only two reference that had been given here, since both these links appear to be broken:
Describing the arrangements which have been made for funding of the nLab in collaboration with the Topos Institute. The page, linked to from the home page, is intended to be fairly general; specific requests for donations can be made elsewhere.
replaced broken
- Marta Bunge, Steve Lack, van Kampen theorem for toposes (ps)
with full text
- Marta Bunge, Steve Lack, van Kampen theorem for toposes, Advances in Mathematics, 179 (2), 2003, Pages 291-317, doi:10.1016/S0001-8708(03)00010-0
Stub for topological string with redirect topological string theory.
stub for type II geometry
added pointer to:
added to van Kampen theorem a clean statement for the group-version
Created new article for stable Yang-Mills connections. (The english and german Wikipedia article are now also available.)
Created new article for stable Yang-Mills-Higgs pairs. (The english and german Wikipedia article are now also available.)
Created article for the Yang-Mills-Higgs equations. (The german Wikipedia article is now also available.)
Added references about the Yang-Mills-Higgs equations.
added pointer to today’s
added publication data to
and pointer to section 11.1 there for Kaehler structures as torsion-free -structures
starting something on the concept introduced in
Sergei O. Ivanov, Roman Mikhailov: A higher limit approach to homology theories, Journal of Pure and Applied Algebra 219 6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]
Sergei O. Ivanov, Roman Mikhailov: Higher limits, homology theories and -codes, in: Combinatorial and Toric Homotopy, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]
but for the moment there is little more than these references
Zoran,
I wanted to add a reference to holomorphic Chern-Simons theory, only to realize that the entry didn't exist yet. Didn't you recently write something about holomorphic CS? I can't find it right now...
created Hadamard lemma
Added an article
Added a “warning” for something that tripped me up: the classifying topos of a classical first-order theory is typically not Boolean, even though the classifying pretopos is Boolean. For a topos to be Boolean is much stronger – as Blass and Scedrov showed, it implies -categoricity.
created a currently fairly empty entry quantum measurement, just so as to have a place where to give a commented pointer to the article
the entry group algebra had been full of notation mismatch and also of typos. I have reworked it now.
I have split off complex projective space from projective space and added some basic facts about its cohomology.
Added doi and pointer to relevant sections to
Marcelo Aguilar, Samuel Gitler, Carlos Prieto, section 6 of Algebraic topology from a homotopical viewpoint, Springer (2002) (toc pdf, doi:10.1007/b97586)
(EM-spaces are constructed in section 6, the cohomology theory they represent is discussed in section 7.1, and its equivalence to singular cohomology is Corollary 12.1.20)
wrote Maurer-Cartan form
the first part is the standard story, but I chose a presentation which I find more insightful than the standard symbol chains as on Wikipedia.
then there is a section on Maurer-Cartan forms on oo-Lie groups and how that reduces to the standard story for ordinary Lie groups.
The detailed statements and proofs of this second part are at Lie infinity-groupoid in the new section The canonical form on a Lie oo-group that is just a Lie group.
added to convenient vector space a Properties-section mentioning their embedding into the Cahiers topos, and added the reference by Kock where this is proven.
a bare list of references, to be !include-ed into the References-sections of relevant entries, for ease of synchronization (at exceptional field theory, exceptional geometry, sigma-model and maybe super p-brane)
Added a reference to the following which provides a proof of the Arnold conjecture
added to exceptional generalized geometry two examples of reductions of stucture groups that encode higher supersymmetry in 11d sugra.
added to tmf a section that gives an outline of the proof strategy for how to compute the homotopy groups of the -spectrum from global sections of the -structure sheaf on the moduli stack of elliptic curves.
A point which I wanted to emphasize is that
The problem of constructing as global sections of an -structure sheaf has a tautological solution: take the underlying space to be .
From this tautological but useless solution one gets to the one that is used for actual computations by one single crucial fact:
In the -topos over the -site of formal duals of -rings, the dual of the Thom spectrum, is a well-supported object. the terminal morphism
in the -topos is an effective epimorphism, hence a covering of the point.
Using this we can pull back the tautological solution of the problem to the cover and then compute there. This is what actually happens in practice: the decategorification of the pullback of to is the moduli stack of elliptic curves. And it is a happy coincidence that despite this drastic decategorification, there is still enough information left to compute on that.