Questions tagged [grothendieck-construction]
The grothendieck-construction tag has no usage guidance.
8
questions with no upvoted or accepted answers
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Grothendieck construction and coends
In category theory, both the Grothendieck construction and coends are represented by a sort of "integral sign", respectively:
$$
\int F
$$
for a functor $F:C\to\mathbf{Cat}$,
and:
$$
\int^x G(x,x)
$$
...
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The category of elements corresponding to a coend as a higher colimit
Let $D: \mathcal{C} \to \mathbf{Set}$ be a diagram of sets, then we can obtain the colimit of $D$ as the set of connected components of the category of elements of $F$, which we denote by $\mathrm{el}(...
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Freely adding comprehensions
If $P:T^{\rm op}\to \rm Cat$ is a hyperdoctrine with at least products in the fiber categories, then there is a way of "freely" adding Lawvere-style comprehension to it. The base category $...
6
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Grothendieck problem
Could you suggest me a book or a link where I can find some information about the Grothendieck problem about differential equations?
The Grothendieck problem that I am reffering to is the following: ...
5
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When is a Grothendieck construction a presheaf category?
Let $C$ be a small category, $\mathcal{P}C$ its presheaf category, and $F:\mathcal{P}C^{\rm op} \to \rm Cat$ a pseudofunctor. Are there general conditions we can impose ensuring that the Grothendieck ...
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Homology and Burnside ring
If $G$ is a finite groupe, we denote $\mathcal{S}(G)$ the category of finite $G$-sets and $\mbox{I}(G)$ the set of isomorphism classes of it's objects. The Burnside ring of $G$, denoted by $\Omega(G)$,...
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Reference request: Grothendieck construction for $\mathbb V$-distributors?
I'm currently working with an analogue of the Grothendieck construction for enriched categories:
Given a distributor a.k.a. $\mathbb V$-functor $D:X^\mathrm{op}\otimes Y\to \mathbb V$ there is a ...
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Composition of Cat-valued distributors - compatible with grothendieck construction?
Let $C$ be a category and $F\in[C^{op}, Cat]$ be a strong functor.
(1) There are functors
$$hom_C(c',c)\times F(c)\to F(c').$$
(2) The grothendieck construction gives a 2-equvalence
$$\int_C: [C^{...