Questions tagged [sketches]
For question on and related to sketches in the technical sense of category theory.
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Is there a large colimit-sketch for topological spaces?
Question. Is there a large colimit-sketch $\mathcal{S}$ such that $\mathrm{Mod}(\mathcal{S}) \simeq \mathbf{Top}$?
In other words, is there a category $\mathcal{E}$ with a class of cocones $\mathcal{S}...
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How to model (affine) schemes with a large sketch?
Guitart states in "Toute theorie est algebrique et topologique" as Proposition 17 that the category $\mathbf{Sch}$ of schemes is the category of models of a large mixed sketch. Presumably, ...
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On Sketches and Institutions
There seems to be two competing(?) formalisms for specifying theories: sketches (as developped by Ehresmann and students, and expanded upon by Barr and Wells in, for example, Toposes, Triples and ...
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Example: Accessible category without colimits
I am looking for intuitive examples of the way(s) that colimits may fail to exist in the category of (Set-valued) models for a limit/colimit sketch.
Bonus points if the sketch and/or the colimit ...
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Example of a non-cocomplete model category of a realized limit sketch
Let $(\mathcal{E},\mathcal{S})$ be a realized limit sketch, i.e. a locally small category $\mathcal{E}$ with a class $\mathcal{S}$ of limit cones in it. It is not assumed that $\mathcal{E}$ is small, ...
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Sketches for categories of models of complete theories
In Accessible categories : the foundations of categorical model theory, chapter 3 p.58, Makkai and Paré claim that there is "an (obvious) identification of a class of sketches so that the categories ...
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How does Gabriel–Ulmer duality extend to (limit, colimit) sketches?
$\newcommand\Sketch{\mathit{Sketch}}\newcommand\Set{\mathit{Set}}
\DeclareMathOperator\Lim{Lim}\DeclareMathOperator\Colim{Colim}\DeclareMathOperator\Mod{Mod}\newcommand\mod{\operatorname{mod}}\...
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How to turn a limit sketch into an essentially algebraic theory?
An essentially algebraic theoery, according to Adamek and Rosicky (second definition on nlab), consists of a many-sorted signature $\Sigma$ (consisting of function symbols on sorts $S$), a set $E$ of ...
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Can such categorical notion of action be formalized?
I'm wondering if it's possible to find an universal construction for a general concept of action for (single-sorted?) finite product sketches, such that one of those is "acting" on the second in the ...
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finite limit sketches with specified maps
Let $C$ be a category. Roughly, a model of a (finite) limit sketch in $C$ is a functor $S \to C$ where $S$ small category with some specified (finite) cones which are sent to limits in $C$. $S$ itself ...
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Define a sketch $s_{\mathbf{Grp}}$ such that $\mathbf{Grp}\backsimeq \mathbf{Mod}(s_{\mathbf{Grp}},\mathbf{Set})$
I have this MSE question with a two hundred bounty but even with the bounty this post got underviewed. So maybe here is a more suitable place to post it. The question follows:
(a) Define a sketch $s_{...
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A notion of limit sketches that makes theories unique up to equivalence
There are multiple ways to formalize the notion of a (limit) sketch, which are basically equivalent. This makes it a bit difficult to decide on a "right way" to formalize sketches. One nice property ...
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Sketch of sketches, or sketch of presentations
In Sketches: Outline with References 4.3, Wells cites the result that sketches are sketchable by a finite limit sketch. I can't find the Burroni 1970a paper, and I am having a lot of trouble with Lair ...
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