# Tagged Questions

**6**

votes

**3**answers

342 views

### Do any Stone-like dualities have some self-dualities hidden inside them?

This question originated from the observation that in most cases when one has duality of structured sets induced by a dualizing set-with-two-structures $D$, both sides of the duality are substructures ...

**11**

votes

**1**answer

175 views

### Looking for concrete description of a category derived from abelian groups

The category of abelian groups $\mathsf{Ab}$ is the $\mathcal{Ind}$-completion of the full subcategory of finitely presentable abelian groups $\mathsf{Ab}_{fp}$. This is not so special, since the ...

**10**

votes

**1**answer

275 views

### Which categories are the categories of models of a Lawvere theory?

Background: a Lawvere theory $T$ is a category with finite products such that each object is a power of a fixed object $x$. Given a Lawvere theory $T$, the category $\text{Mod}_T$ of models of $T$ is ...

**8**

votes

**0**answers

239 views

### Twisted duality in a symmetric monoidal category

I would like to know if the following definition is already known or even well-known. Is there a reference in the literature? Do you know prominent examples?
Definition. Let $\mathcal{C}$ be a ...

**5**

votes

**3**answers

258 views

### Why are possibility and necessity dual?

Hello,
Recently, I'm studying modal logic for my master's thesis, and my research background is category theory.
So, I naturally have a question that why it is said that necessity (box) and ...

**2**

votes

**1**answer

355 views

### A category being self-dual vs. it being a groupoid

What is the relationship between self-duality and groupoid-ness? Does any condition imply the other? Is there an example which helps understand the difference?
To go from a self-duality $F$ on a ...

**0**

votes

**1**answer

442 views

### a “self-dual” adjunction

Is there a name for $(U,\eta)$ such that $(\eta, \eta^{op}):U^{op}\dashv U$ (is an adjunction). To clarify — $C:category$, $(I,I^{op})$ is the contravariant isomorphism with $I:C^{op}\to C$, ...