# Tag Info

### Is the term "category" in Category theory entirely different from the category in topological spaces?

Perhaps disappointingly, there is no connection between the two uses at all. (Given this, I prefer to use "meager" for "first category," and my impression is that this is pretty ...
• 218k
Accepted

### How do natural transformations capture a "lack of arbitrarity"/uniqueness?

• 8,561

### What is the right adjoint to the functor $\sf{Psh}\to\sf{Set}$ which evaluates the presheaf on the whole space?

As you have already figured out, the functor $Γ$ is the “global sections” functor that evaluates a presheaf $F$ on the entire space $\mathcal{T}$. The desired right adjoint $∇$ of $Γ$ needs to assign ...
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### What is the right adjoint to the functor $\sf{Psh}\to\sf{Set}$ which evaluates the presheaf on the whole space?

Here is a method to find the answer without "having to guess". The essential point is that the functor of sections over an open subset $U \subseteq X$ (where $X$ is a topological space) is ...
• 15.5k