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$\def\Spec{\mathop{\rm Spec}} \def\R{{\bf R}} \def\Ep{{\rm E}^+} \def\L{{\rm L}} \def\EpL{\Ep\L}$ One can argue that an object of the right category of spaces in measure theory is not a set equipped w …

Daniel M. Kan defined adjoint functors in his paper Adjoint functors (written in 1956). In Chapter II he defines limits and colimits of arbitrary small diagrams and proves that the limit and colimit f …

A spin structure on a real vector space V equipped with a real quadratic form μ is an invertible bimodule (i.e., a Morita equivalence) from Cl(V,μ) to Cl(Rdim(V),ν). Here ν is the direct sum of dim(V) …

A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n. Is there a citeable reference for a proof of this result? For the sake of being definite, let's say that “citeable” m …

Boardman's thesis was (re)published a year later as three separate booklets, and a PDF scan of all three booklets is available on my scans page: J. M. Boardman. Stable homotopy theory. University of W …

“Diffeology” by Patrick Iglesias-Zemmour is probably the closest match. He develops differential forms and de Rham cohomology, fiber bundles, connections, and symplectic geometry in the language of di …

This might be irrelevant, but I would like to point out that if one restates Hahn-Banach theorem in the language of locales (replacing topological spaces), one can get rid of the axiom of choice and t …

There is a short elementary survey by Hohnhold, Stolz, and Teichner: Super manifolds: an incomplete survey.

1 and 3 are proved in Appendix A of the book “Algebraic theories” by Jiří Adámek, Jiří Rosický, Enrico M. Vitale. 1 is Theorem A.37 (and A.41 for the multisorted version). 3 is Theorem A.21 (and A.40 …

Apparently this is the book that contains your paper: http://www.worldcat.org/title/problemy-povysheniia-effektivnosti-raboty-transporta/oclc/28097589&referer=brief_results It's also present in Googl …

Chris Douglas has a nice short discussion of homotopy limits in his text “Sheaves in homotopy theory” (Chapter 5 of Topological modular forms).

Answers: (i) Yes, if we replace states by weights (not every von Neumann algebra admits a faithful state); (ii) Yes (for all von Neumann algebras); (iii) All of them. Suppose M is an arbitrary von Ne …

Yes, it is also available here: https://www.math.uni-bielefeld.de/sfb343/preprints/pr97044.ps.gz

To answer the first question: there are two completely elementary proofs of the existence of differentiable good open covers: the first one is Lemma IV.6.9 in Demailly's “Complex Analytic and Differen …

The usual constructions of Grothendieck homotopy theory (as presented by Maltsiniotis and Cisinski) can be easily extended to the setting of relative categories. Recall that given a small category $A$ …