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1d
reviewed Reviewed Learning roadmap in Algebra
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comment Three questions on $\operatorname{hocolim}$
(continuation) The preceding counter-example is very similar to the one in the second part of my answer above. However, there is a sub-object of the 1-truncation of the bar construction which will compute the homotopy colimit of $F$: at level one, consider only the morphisms $n \to n+1$ for $n\in\mathbb{N}$, and remove all other morphisms from the 1-truncated bar construction. The realization of this sub-object is precisely the mapping telescope of the functor $F$, and is therefore equivalent to the homotopy colimit of $F$.
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comment Three questions on $\operatorname{hocolim}$
Dear @jeffrey, in the case of the category $\newcommand{\NN}{\mathbb{N}} \NN$, we cannot compute the homotopy colimit of a functor $F:\NN\to\mathrm{sSet}$ using the 1-truncation of the bar construction $B(F,\NN,\ast)$ (this bar construction is precisely the "$\coprod$-thing"). In fact, the realization of that 1-truncation for $F=\ast$ is the 1-skeleton of the classifying space of $\NN$, which consists of the set $\NN$ with one segment added between each pair of distinct points of $\NN$. This space is not contractible, thus cannot be the homotopy colimit of $F=\ast$. (to be continued...)
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reviewed Leave Closed Question about continuity of Holder functions
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reviewed Close Are major arcs always around a fraction with small denominator?
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awarded  Enlightened
1d
awarded  Nice Answer
1d
revised Can a birational morphism between smooth varieties be dominated by smooth blowup sequences?
removed deprecated tag 'geometry'
Sep
17
reviewed Leave Closed Find the volume generated by revolving
Sep
17
reviewed Reviewed Generate Gamma random number using scale or rate parameters
Sep
17
reviewed Reopen For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
Sep
17
reviewed Close Question about continuity of Holder functions
Sep
17
revised What's the relation between fusion and coproduct?
removed tag 'tag-removed'; added top-level tag
Sep
16
reviewed Close What does it mean for a stochastic sequence to be “stochastically smaller” than some other stochastic sequence?
Sep
15
revised Eigenstates of Fourier transformation
replaced new tag 'fourier'
Sep
15
revised Decomposition of Lefschetz fibrations into surface bundles and Lefschetz fibrations over spheres
replaced deprecated tag 'geometry'
Sep
15
reviewed Close Does this integral have a closed form?
Sep
15
revised Does this integral have a closed form?
replaced deprecated tag 'calculus'
Sep
14
comment How do I calculate adjoint functors to forgetful functors?
Please do not post questions simultaneously to MathOverflow and to Math.StackExchange. It leads to duplication of effort and is frowned upon by both communities. Please pick one of the sites and wait at least a few days for an answer before reposting the question elsewhere. Thank you. That being said, the present question is not research-level and is more appropriate on Math.StackExchange.
Sep
14
reviewed Close How do I calculate adjoint functors to forgetful functors?