# ct.category-theory's questions - English 1answer

3.670 ct.category-theory questions.

### 4 Homotopy limit of model categories in the category of categories

Say $$\mathcal{C'}\to \mathcal{C}\leftarrow \mathcal{D}$$ is a diagram of model categories and (e.g. Left) Quillen functors. I want to write down a (hopefully simple) model category $\mathcal{D}'$, or ...

### 16 Is Feferman's unlimited category theory dead?

0 answers, 707 views ct.category-theory lo.logic foundations
In The prospects of unlimited category theory: doing what remains to be done, 2014 (The Review of Symbolic Logic, 8 (2015) pp 306-327, link), Ernst discusses Feferman's program, described in ...

### 4 Extending a functor up to homotopy

Consider a functor between small categories $i:\mathcal{A}\to \mathcal{B}$ which is faithful, not full, and bijective on objects. Consider a functor $F:\mathcal{A}\to \mathcal{M}$ where $\mathcal{M}$ ...

### 3 Calculating the intersection of the saturations of a decreasing sequence of morphisms

I have a sequence $W_0\supset W_1\supset \ldots$ of classes of morphisms in a presentable $(\infty,1)$-category $\mathcal{M}$. I can present this $(\infty,1)$-category as a model category, but I'm ...

### 2 Left Kan extension and extension of functors

Consider a functor $F:\mathcal{A}\to \mathcal{B}$ between two small categories. Let $\mathcal{K}$ be a locally presentable category. Consider a functor $G:\mathcal{A}\to \mathcal{K}$, there is a ...

### 5 General existence theorem for cup products

I'm curious if it is possible to formulate cup products and prove that they exist in a general way which would subsume a lot of examples: e.g. group cohomology, sheaf cohomology for sheaves on ...

### 25 Why are monadicity and descent related?

This question is probably too vague for experts, but I really don't know how to avoid it. I've read in several places that under mild conditions, a morphism is an effective descent morphism iff the ...

### 4 The Yoneda embedding induces a monad-like structure?

This question was already asked on MSE. In CAT the Yoneda embedding $C^{\text{op}} \stackrel{y_C}{\to} \text{hom}(C, \text{Set})$, induces a map \text{hom}(\text{hom}(C, \text{Set}), \text{Set}) \...

### -2 Are database tables multispans?

0 answers, 79 views ct.category-theory database-theory
Spivak has done work showing that database schemas are categories. I am thinking of basic database tables and how the primary key binds all the columns together. If there were only two columns, ...

### 11 What is the monoidal equivalent of a locally cartesian closed category?

If a closed monoidal category is the monoidal equivalent of a Cartesian closed category, is there an analogous equivalent for locally cartesian closed categories? Is there a standard terminology or ...

### 19 Defining computable functions categorically

Computable functions may be defined in terms of Turing machines or recursive functions, or some other model of computation. We normally say that the choice doesn't matter, because all models of ...