bio | website | dpmms.cam.ac.uk/~zll22 |
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location | ||
age | ||
visits | member for | 3 years, 11 months |
seen | 2 hours ago | |
stats | profile views | 2,868 |
Nov 11 |
comment |
Infinity category of functors from a relative category to a model category
The special case $\mathcal{M} = \mathbf{sSet}$ is addressed implicitly in [Dwyer and Kan, Equivalences between homotopy theories of diagrams]. |
Nov 4 |
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The real numbers object in Sh(Top)
Don't we need it to deduce that $\mathbf{Geom}(\mathbf{Sh}(Y), \mathbf{Sh}(\mathbb{R}))$ is equivalent to the set $\mathbf{T}(Y, \mathbb{R})$? |
Nov 4 |
answered | The real numbers object in Sh(Top) |
Nov 3 |
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Infinite Fubini rule for co/limits
It's really easy: if you have $f_n : X_n \to X_{n+1}$ then the transfinite composition $\cdots \circ f_2 \circ f_1 \circ f_0$ lands in $\varinjlim_n X_n$. |
Nov 3 |
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Infinite Fubini rule for co/limits
No, you can't just do transfinite composition here. That would land in some other category. |
Nov 3 |
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Infinite Fubini rule for co/limits
I think there's more than just a notational problem here. How do you define infinitely iterated colimits? |
Nov 2 |
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Image, kernel, quotient and first isomorphism theorem, in a category of monoid objects
@QiaochuYuan The trivial monoid with respect to a cartesian monoidal structure is a zero object, yes. But consider for instance $\mathbb{Z}$ as a monoid in $\mathbf{Ab}$... |
Oct 28 |
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Why do filtered colimits commute with finite limits?
It is true. The usual proof uses the fact that sheafification preserves finite limits as well as filtered colimits. |
Oct 23 |
revised |
Characterize the category of rings
added 4 characters in body |
Oct 23 |
answered | Characterize the category of rings |
Oct 21 |
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Higher vector spaces
Well, there is a trivial observation: an idempotent-complete category $\mathcal{C}$ is (equivalent to) the category of finitely presented $R$-modules if and only if $\mathbf{Ind}(\mathcal{C})$ is (equivalent to) the category of $R$-modules. |
Oct 15 |
revised |
$(LLP(Epi), Epi)$ is a WFS on any variety of algebras
added 1 character in body |
Oct 15 |
answered | $(LLP(Epi), Epi)$ is a WFS on any variety of algebras |
Oct 15 |
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$(LLP(Epi), Epi)$ is a WFS on any variety of algebras
$U$ should be only faithful, not fully faithful. |
Oct 15 |
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Cocomplete but not complete abelian category
This looks like the direct limit of an $\mathbf{On}$-indexed sequence of cocomplete abelian categories along colimit-preserving exact functors, so it should be just abstract nonsense that it is a cocomplete abelian category. |
Oct 13 |
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Homotopy uniqueness of some coends
Essential uniqueness here is referring to the fact that some classifying space is contractible. I wouldn't read too much into it. |
Oct 13 |
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Homotopy uniqueness of some coends
But the diagrams in question are indeed cofibrant? |
Oct 11 |
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Question regarding 2-mathematics: Can you stackify a 2-functor without prestackifying it first?
This seems to be a folklore result. It is alluded to in [Higher topos theory, §6.5.3]. |
Oct 9 |
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The Karoubi model structure on Cat
Yes, it is a left Bousfield localisation of the canonical model structure, almost by definition. The generating cofibrations are therefore the same as for the canonical model structure. |
Oct 8 |
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The Karoubi model structure on Cat
I describe the model structure here. There is just one extra generating trivial cofibration, namely the inclusion of the free idempotent into the free split idempotent. |