# Tagged Questions

**14**

votes

**1**answer

602 views

### Lawvere's fixed point theorem and the Recursion Theorem

Building off of Qiaochu's comment on my answer to a previous mathoverflow question, I would like to know: can the Recursion Theorem, $$\forall e\exists k[\Phi_e\text{ is total }\implies ...

**7**

votes

**2**answers

764 views

### Categories of recursive functions

I have a couple of conjectures on recursive functions, that I feel must have been proved or refuted by someone else, but I don't know where to look. In short:
1. The primitive recursive functions ...

**9**

votes

**3**answers

731 views

### Effective topos and computability in topological spaces

The classical computability theory taking place in $\mathbb{N}$, can be extended to more general spaces, like $T_0$ second countable topological spaces $(X, \mathcal{O}, v)$ where $\mathcal{O}$ is a ...

**2**

votes

**0**answers

203 views

### A polytime feasible subuniverse of the Effective Topos

The effective topos is a well known universe of sets suitable for abstract computability, as it is build "from the ground up" via the classical notion of realisability by Kleene.
I have found a few ...

**13**

votes

**2**answers

631 views

### Are the axioms for higher category-theory effectively computable?

I ask this, although I don't conduct any research in the area, or even plan to. -- There seems to be general agreement that the axioms for higher categories grow very rapidly in complexity as the ...

**1**

vote

**2**answers

391 views

### Pullbacks for primitive recursive functions.

Since a pullback of two functions f and g with common codomain into Set category is just a subset of cartesian product like this: {(x,y)/f(x)=g(y)} (with two more functions not important here) could ...

**19**

votes

**3**answers

2k views

### Is the theory of categories decidable?

There are a lot of theorems in basic homological algebra, such as the five lemma or the snake lemma, that seem like they'd be more easily proven by computer than by hand. This led me to consider the ...

**1**

vote

**1**answer

480 views

### Coequalizer in the category of primitive recursive functions

What does a coequalizer in the category of primitive recursive functions look like? I know that in Set, a coequalizer is a minimum congruence but...what is it in particular in the category of ...