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For some time now I’ve been bothered by an implicit redundancy spanned by the articles nice category of spaces and convenient category of topological spaces. I would like the latter to have a more precise meaning and the former to be something more vague and flexible. I have therefore been doing some rewriting at the former. But if anyone disagrees with the edits, please let’s discuss this here.
I have removed a query box:
+– {: .query} I’m not sure that we really want to use the terminology that way, but Ronnie already created that page, so I’m linking these together. —Toby =–
At simplex I have accompanied the definition of the cellular simplex with that of the topological simplex.
Charles Waldo Rezk is a mathematician at the University of Illinois Urbana–Champaign.
He got his PhD degree in 1996 at MIT, advised by Michael J. Hopkins.
His PhD students include Nathaniel Stapleton and Nima Rasekh.
This is a bare list of references, to be !include-ed into relevant entries (such as string phenomenology, heterotic string and GUT), for ease of keeping these entry’s bibliographies in sync
Added pointer to section 7 of
starting some minimum, cross-linking with quaternion-Kähler manifold and Sp(n).Sp(1)
starting something, for the moment just so as to record that
there is a homeomorphism
between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.
Asked a question at natural transformation.
had occasion to create dual vector space.
I added to initial object the theorem characterizing initial objects in terms of cones over the identity functor.
for the Café-discussion I added to zero object the details of the proof that in a -enriched category every terminal or initial object is zero.
In the course of this I did a bit of brushing-up of a bunch of related entries. For instance at pointed set I made the closed monoidal structure on manifest, etc.
Wrote a bunch of stuff on determinant. Just because I felt like it. But I’ve run out of steam to do more on it now.
I changed the name of the page Frobenius map to Frobenius morphism and added the descriptions à la Demazure to it.
Adding reference
as a construction of the locale of real numbers can be found in section 5.3 of that article
Anonymous
Added to one-sided real number a short discussion of the correspondence of internal lower reals in a sheaf topos and upper semicontinuous functions .
Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.
I made Cayley plane a little less stubby.
added pointer to today’s
New stub, Gauss-Manin connection.
finding that an entry like this has been missing all along (all we seem to have had was this paragraph at enriched category) I have now created it with some minimum content, for completeness
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)
Created a stub for Urysohn metrization theorem.
stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)
I’ve removed this query box from metric space and incorporated its information into the text:
Mike: Perhaps it would be more accurate to say that the symmetry axiom gives us enriched -categories?
Toby: Yeah, that could work. I was thinking of arguing that it makes sense to enrich groupoids in any monoidal poset, cartesian or otherwise, since we can write down the operations and all equations are trivial in a poset. But maybe it makes more sense to call those enriched -categories.
added reference to derived category
I felt there should be an entry category of presheaves. So I started one.
added pointer to:
David Jaz Myers, String Diagrams For Double Categories and (Virtual) Equipments [arXiv:1612.02762]
David Jaz Myers, String Diagrams for (Virtual) Proarrow Equipments (2017) [slides: pdf]
New entry prime spectrum with redirect Zariski spectrum.