# Questions tagged [categorical-logic]

Categorical logic is a study of semantics constructed by categories.

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### Defining truth in a topos model

My colleague and I are working through Goldblatt's Topoi, and we're stuck on exercise 2 in chapter 11, section 4. The exercise is to show that $\|\phi\|^m \circ f = \|\phi\|^m \circ h$, for any ...
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### What is a logical formula in the language of categories? How can we express basic model theoretic concepts categorically?

At the beginning of a course in Model Theory, one is introduced to the definition of signature, structure and homomorphism. It is then clear that the class of all structures over a fixed signature $L$ ...
57 views

### Syntactic category of a geometric theory has finite limits.

Let $T$ be a geometric theory. Consider the syntactic category $C_T$. I want to show that $C_T$ has all finite limits. To show this, it is enough to show that it has finite products and equalizers. ...
171 views

### The legitimacy of topos theory and intuitionism.

This is an exercise in critical thinking. I am not looking, therefore, for opinions on the matter; rather: I would like to know the evidence (whatever that might mean). Background: I have a ...
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### Which limit sketches produce Grothendieck toposes?

A limit sketch $\mathcal S=(\mathcal A,L)$ consists of a small category $\mathcal{A}$, together with a set $L$ of cones in $\mathcal A$. A model (in the category of sets) of a limit sketch is a ...
122 views

### Logic and adjunctions with ideals in ring theory

Studying ring theory, I remarked two things in the context of ideals that look like some interpretation of a logic in the ideals of a ring (I never studied this subject so my formulation is quite ...
107 views

### Sorting out what's true in the generic model in the classifying topos of a theory

I'm interested in trying to understand the generic model in the classifying topos of a particular coherent theory$^1$, and more specifically trying to sort out what non-coherent formulae hold in said ...
88 views

### Hyperdoctrines and Contravariance

I've been reading through the extremely useful discussion of First-Order Categorial Logic that recently popped up over at The Diagonal Argument. But when I compare Baez and Weiss's construction to ...
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### How to construct a regular functor from a categorical interpretation?

I have read a lecture note by Jaap van Oosten and I am stuck on the exercise 84 in the article. A functor between two regular categories is regular if it preserves finite limits and regular ...
231 views

### How to express predicate logic in the categorical (monoidal) logics?

Rosetta stone in the book "New Structures in Physics" (http://www.springer.com/la/book/9783642128202) is the correspondence between the propositional (linear) logic from the one side and the monoidal ...
200 views

### Path to categorical realizability theory

I'm trying to understand the sorts of things found on this page: http://ncatlab.org/nlab/show/realizability In particular, I want to read Oosten's Realizability: An Introduction to the Categorical ...