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This tag is used if a reference is needed in a paper or textbook on a specific result.

8 votes

Trying to find a 1949 Russian Paper on Transportation Theory

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 …
Dmitri Pavlov's user avatar
3 votes

Trying to find a 1949 Russian Paper on Transportation Theory

Here is the scanned book: http://math.berkeley.edu/~pavlov/scans/transport.pdf Enjoy. Please consider putting it on your home page (if you have one) so that other scientists who need this book in the …
Dmitri Pavlov's user avatar
4 votes
Accepted

Topologizing the category of measure spaces

As demonstrated by Andre Kornell in http://arxiv.org/abs/1202.2994, the category of measurable spaces is closed with respect to the monoidal structure given by the spatial tensor product (Theorem 9.5) …
Dmitri Pavlov's user avatar
2 votes
Accepted

Simplicial Objects in Additive Categories

For abelian categories this is known as the Eilenberg–Zilber theorem, see, for instance, Theorem 8.5.1 in Weibel's book. One can write down explicit comparison maps in both directions (namely, the Ale …
Dmitri Pavlov's user avatar
2 votes
Accepted

Any reference including a coordinate free proof of the inverse function theorem?

A coordinate-free proof of the inverse function theorem in the finite-dimensional case is provided by Theorem 19.6 in "Topological Geometry" by Ian R. Porteous. In general, the cited book is an expos …
Dmitri Pavlov's user avatar
2 votes
Accepted

A question about possibly $\infty$-category or functors

$T$ can be formalized as a natural transformation $\def\Vect{{\rm Vect}} \def\Vectc{\Vect_\nabla} \Vectc→Ω^n$ of functors $\def\Man{{\sf Man}} \def\op{{\sf op}} \def\Grpd{{\sf Grpd}} \Man^\op → \Grpd$ …
Dmitri Pavlov's user avatar
5 votes

Original reference for generators and relations of 2-dimensional TQFT

Generators and relations for the nonextended 2-dimensional bordism category already appear in Robbert Dijkgraaf's 1989 PhD dissertation, see Section 3.2.
Dmitri Pavlov's user avatar
2 votes
Accepted

Looking for Celeyrette's PhD thesis, "Fibrations et extensions de Kan"

There are two theses by Jean Celeyrette indexed by various libraries: Theoreme de Kan dans un topos (Lille, 1974). Catégories internes et fibrations ; Cohomologie de Gel'fand-Fuks (Paris-Nord, 1975). …
Dmitri Pavlov's user avatar
6 votes

A Learning Roadmap request: From high-school to mid-undergraduate studies

Here is my list. I tried to make it more practical by supplying links to electronic versions whenever possible. Rudin: Principles of mathematical analysis Electronic version: http://libgen.org/get?n …
1 vote

A question on the ring structure of topological K-theory and Chern character

The product of $K^{−1}$ with itself can be defined by identifying $K^{−1}(X)$ with $K^0(X\wedge S^1)$ using the suspension isomorphism, multiplying the resulting two elements of $K^0(X\wedge S^1)$, o …
Dmitri Pavlov's user avatar
6 votes
Accepted

Weak composition rule for simplicial categories

The most obvious approach is to consider simplicial $\def\Ai{{\sf A}_∞}\Ai$-categories, where $\Ai$ denotes a nonsymmetric operad in simplicial sets that is weakly equivalent to the terminal operad, i …
Dmitri Pavlov's user avatar
2 votes
Accepted

Homologous quotient of fundamental groupoid

The resulting groupoid is equivalent to the disjoint union of groupoids $B(H_1(X_i))$ taken over all connected components $X_i$ of $X$. This answers both 1 and 2 in the positive. To see this, observe …
Dmitri Pavlov's user avatar
2 votes

Representing simplicial homotopy classes by empty cubes

Yes. The map ∂◻^{n+1}→S^n that collapses the complement of a single n-dimensional face of ◻^{n+1} is a simplicial weak equivalence. This implies that the induced map Map(S^n,K)→Map(∂◻^{n+1},K) is a s …
Dmitri Pavlov's user avatar
7 votes

Relative category structure on (Set valued) presheaves

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 $A$ …
Dmitri Pavlov's user avatar
4 votes
Accepted

Is the standard model structure on reduced simplicial sets cofibrantly generated?

Yes, the model structure on reduced simplicial sets is cofibrantly generated. An explicit proof of this statement is given by Goerss and Jardine in Simplicial Homotopy Theory, the proof of Proposition …
Dmitri Pavlov's user avatar

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