# Tagged Questions

**2**

votes

**0**answers

106 views

### Which reflexive coequalizer diagrams are projectively cofibrant?

Consider the walking reflexive pair category W,
which consists of two objects 0 and 1 and three generating
morphisms f: 0→1, g: 0→1, and h: 1→0
satisfying the relation fh=gh=id₁.
Consider the ...

**4**

votes

**1**answer

319 views

### When do reflexive coequalizers preserve weak equivalences?

In my work I've run into the following situation. In a model category, I have two reflexive coequalizers $A_i \stackrel{\to}{\to} B_i \to C_i$ and a map of diagrams which is levelwise a weak ...

**10**

votes

**2**answers

439 views

### Fubini theorem for hocolim.

I wanted to ask the following question,
Suppose $\mathbf{M}$ a cof generated model category and $I,~J$ two small categories. Suppose that $F:J\rightarrow \mathbf{M}^{\mathrm{I}}$ is a functor. Is it ...

**5**

votes

**2**answers

517 views

### Is the category of small categories locally presentable?

I was wondering whether the various model structures on the category of small categories are combinatorial. I think that the ones I know are at least cofibrantly generated. In order to be ...

**6**

votes

**1**answer

418 views

### How does Berger-Moerdijk's relative Boardman-Vogt work?

In "The Boardman-Vogt resolution of operads in monoidal model categories," the authors construct factorizations of sufficiently nice operad maps $P\to Q$ into a cofibration followed by a weak ...