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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
A bare list of references, to be !include-ed into the References-subsection of relevant entries
(This list used to be hard-coded at supergravity C-field but since it also deserves to be included at D=11 supergravity and maybe elsewhere, I am splitting it off this way, for ease of synchronization.)
I added to category of elements an argument for why preserves colimits.
created a brief entry IKKT matrix model to record some references. Cross-linked with string field theory, and with BFSS matrix model
started a stubby nPOV-description at the beginning of BV-BRST formalism
somebody please stop me, though, because I urgently need to be doing something else... :-)
created a bare minimum at light-cone gauge quantization, just so as to be able to sensibly link to it from elsewhere
started some minimum at weak gravity conjecture
I tried to brush-up the References at period a little.
I have trouble downloading the first one, which is
My system keeps telling me that the pdf behind this link is broken. Can anyone see it? (It may well just be my system misbehaving, wouldn’t be the first time…).
Added reference
Anonymouse
Added reference
note that the website linked on this page doesn’t work anymore
Anonymouse
I created a stub page for Douglas Bridges. I linked to his home page but also to a page on FAQs in constructive mathematics. He seems to have other stuff there and there may be other useful links worth creating.
I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to
added to partial function a new section Definition – General abstract with a brief paragraph on how partial functions form the Kleisli category of the maybe-monad.
Added reference
Anonymouse
I added a new section to algebraically closed field, on the classification in terms of characteristic and transcendence degree.
I looked at real number and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:
A real number is something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form a number field, denoted . The underlying set is the completion of the ordered field of rational numbers: the result of adjoining to suprema for every bounded subset with respect to the natural ordering of rational numbers.
The set of real numbers also carries naturally the structure of a topological space and as such is called the real line also known as the continuum. Equipped with both the topology and the field structure, is a topological field and as such is the uniform completion of equipped with the absolute value metric.
Together with its cartesian products – the Cartesian spaces for natural numbers – the real line is a standard formalization of the idea of continuous space. The more general concept of (smooth) manifold is modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (see spacetime), or at least in classical physics. See at geometry of physics for more on this.
I edited Trimble n-category:
added table of contents
added hyperlinks
moved the query boxes that seemed to contain closed discussion to the bottom. I kept the query box where I ask for a section about category theory for Trimble n-categories, but maybe we want to remove that, too. Todd has more on this on his personal web.
I wrote out a proof which uses very little machinery at fundamental theorem of algebra. It is just about at the point where it is not only short and rigorous, but could be understood by an eighteenth-century mathematician. (Nothing important, just fun!)
added a bit more text to the Idea-section at Wick rotation and in particular added cross-links with Osterwalder-Schrader theorem.
Created:
[…]
Fredrik Dahlqvist, Vincent Danos, Ilias Garnier, and Alexandra Silva, Borel kernels and their approximation, categorically. In MFPS 34: Proceedings of the Thirty-Fourth Conference on the Mathematical Foundations of Programming Semantics, volume 341, 91–119, 2018.
Tobias Fritz, A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics. Adv. Math., 370:107239, 2020. arXiv:1908.07021.
Noé Ensarguet, Paolo Perrone, Categorical probability spaces, ergodic decompositions, and transitions to equilibrium. arXiv.
definition as described in
I’m making some edits to locally finitely presentable category, and removing some old query boxes. A punchline was extracted, I believe, from the first query box. The second I don’t think is too important (it looks like John misunderstood).
+–{: .query} Mike: Do people really call finitely presentable objects “finitary”? I’ve only seen that word applied to functors (those that preserve filtered colimits). Toby: I have heard ’finite’; see compact object. Mike: Yes, I’ve heard ’finite’ too. =–
+– {: .query} Toby: In the list of equivalent conditions above, does this essentially algebraic theory also have to be finitary?; that is, if it's an algebraic theory, then it's a Lawvere theory?
Mike: Yes, it certainly has to be finitary. Possibly the standard meaning of “essentially algebraic” implies finitarity, though, I don’t know. Toby: I wouldn't use ’algebraic’ that way; see algebraic theory. John Baez: How come the first sentence of this paper seems to suggest that the category of models of any essentially algebraic theory is locally finitely presentable? The characterization below, which I did not write, seems to agree. Here there is no restriction that the theory be finitary. Does this contradict what Mike is saying, or am I just confused?
Mike: The syntactic category of a non-finitary essentially algebraic theory is not a category with finite limits but a category with -limits where is the arity of the theory. A finitary theory can have infinitely many sorts and operations; what makes it finitary is that each operation only takes finitely many inputs, hence can be characterized by an arrow whose domain is a finite limit. I think this makes the first sentence of that paper completely consistent with what I’m saying. =–
definition as per
added an Idea-section to moduli stabilization
Stub. For now just recording links which go beyond the scope of arithmetic cryptography.
added pointer to
for discussion of monopole correlation functions.
Really I am looking for discussion of caloron correlation functions, though…
stub for N=4 D=3 super Yang-Mills theory…
… for the moment just so as to be able to reference the literature on the flavor of S-duality needed at symplectic duality.
moved information on extension types from type theory with shapes to its own page
Added more material to Boolean algebra, particularly the principle of duality and the connection to Boolean rings, and a wee bit of material on Stone duality.
Stone duality deserves greater expansion, bringing out the dualities via ambimorphic (ahem, schizophrenic) structures on the 2-element set, and mentioning the connection to Chu spaces. Another day, another dollar.