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Results tagged with ct.category-theory
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user 9684
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
5
votes
Accepted
What is the intuitive difference between these two simplicial subdivision functors?
Lemma 2.2.11 in mn.uio.no/math/personer/vit/rognes/papers/aoms186-nocrop.pdf shows that the surjection you denote $sd(X) \to S(X)$ is an isomorphism if and only if $X$ is a non-singular simplicial set …
- 9,263
21
votes
Accepted
Is this an instance of the snake lemma?
Splice the left ends of the kernel-cokernel exact sequences
$0 \to \ker(f) \to \ker(gf) \to \ker(g) \to \mathrm{cok}(f) \to \mathrm{cok}(gf) \to \mathrm{cok}(g) \to 0$
and
$0 \to \ker(g) \to \ker(kg) …
- 9,263
10
votes
A question about Poincare duality
It is true. For ordinary cohomology this is a standard result about degree one maps; I think it is discussed at the beginning of Browder's book "Surgery on simply-connected manifolds". Let me treat e …
- 9,263
2
votes
Accepted
On the definition of infinity-category
Partial monoids (see Definition 2.2) play a useful role in
Segal, Graeme
Configuration-spaces and iterated loop-spaces.
Invent. Math. 21 (1973), 213–221.
- 9,263
14
votes
Accepted
The "right" topological spaces
The convenient category CGH of compactly generated Hausdorff spaces has some poor colimits, since Hausdorffification may change the underlying point sets. The category CGWH of compactly generated we …
- 9,263
17
votes
Categorification of determinant
You can try to define the determinant of an $n \times n$ matrix with entries in a bipermutative (or symmetric bimonoidal) category $R$ by an analogue of the usual signed sum of $n$-fold products. Howe …
- 9,263
10
votes
What is the relation between the sphere spectrum and supersymmetry?
Like Schreiber does in his post, I would advertise the point of view developed by Sagave and Schlichtkrull in their Adv. Math 2012 paper, and used by us to study topological logarithmic geometry. Each …
- 9,263
5
votes
Accepted
Is there an ∞-categorical interpretation of the Quillen S⁻¹S construction?
A published reference for the claim (right after the question in boldface) is the proof given by Thomason on pages 1657-1658 of "First quadrant spectral sequences in algebraic K-theory via homotopy co …
- 9,263