# Tagged Questions

Various structures are studied in category theory using properties of objects and morphisms between them. Many constructions are special cases of categorical limits and colimits (e.g. products in various categories). The notions of functor and natural transformations are very important in category ...

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### Categorical semantics for dynamic epistemic logic

Dynamic epistemic logic tries to reason about knowledge that certain actors (people, machines, etc.) have and how it can change in response to outside events. It is usually possible to discuss such a ...
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### Which book would you recommended as help (assistance) for reading the so-called “Tohoku Paper”?

Recently I thought that maybe is a good time to try, read Grothendieck's "Tohoku paper" as a sort of inspiration for the future and to read some of the ideas of this great mathematician, which (among ...
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### Different definitions of cartesian closed category?

The following is the definition of a cartesian closed category in Goldblatt's Topoi: Definition 1: A category $C$ is cartesian closed if (1) it is finitely complete, i.e. every finite diagram ...
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### What is the pushout of $\mathbf{1} \longleftarrow \mathbf{2} \longrightarrow \mathbf{1}$?

I wonder what the pushout of the following diagram would be $$\mathbf{1} \stackrel{f}{\longleftarrow} \mathbf{2} \stackrel{g}{\longrightarrow} \mathbf{1}$$(here $\mathbf{1}$ and $\mathbf{2}$ denote ...
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### Noteworthy examples of finite categories

So far all the finite categories I have encountered fall into one of these c̶a̶t̶e̶g̶o̶r̶i̶e̶s̶ sets: finite monoids finite preorders just formal devices to explain, what a "diagram" in another (...
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### Can tensor abelian categories always be embedded into the category of modules?

Let $(\mathcal A, +,\otimes,I)$ a small symmetric monoidal abelian category. I know that $\mathcal A$ can be embedded into the category of $R$-module for a certain ring $R$. But can we make such ...
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### Does this thing I'm calling 'the operationalization of $x$' have an accepted name?

Given a set $X$ and an element $x \in X$, we can turn $x$ into a function denoted $\tilde{x}$ as follows: for any set $Y$ and any function $f : X \rightarrow Y$, define $$\tilde{x}(f) = f(x).$$ For ...
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### Cartesian closed subcategories of compact Hausdorff topological spaces?

The category of compact Hausdorff topological spaces is famously not cartesian closed. I was wondering how much more one has to assume to actually arrive to a cartesian closed category. For example, ...
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### Delooping of a ring?

I'm no expert on category theory, so the definition of delooping in the nlab article is a bit over my head. However, I do understand the practical idea that we can think of a group $G$ as a one-object ...
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### What exactly are the meaning of the followings in the definition of a category?

In Awodey's Category Theory a category is defined as follows. A category consists of the following data, Objects: $A, B, C,\ldots$ Arrows: $f,g,h,\ldots$ For each arrow $f$ there are ...
Let $G$ be a group. We observe the category $(Set)_G$ of right group actions. a) Let $X\times G\to X$ and $Y\times G\to Y$ be two transitive right group actions with $x\in X$ and $y\in Y$. Find a ...