# Tagged Questions

**9**

votes

**1**answer

415 views

### Does this property of a partially ordered set have a name?

What do you call a poset with this property? For any elements $a,b,c,d$ such that $\{a,b\}\le\{c,d\}$, there is an element x such that $\{a,b\}\le x\le\{c,d\}$. (Equivalently, for any finite sets ...

**6**

votes

**0**answers

128 views

### “Double convolution” with the Mobius function on a poset

Let $f$ and $g$ be arbitrary (say integer-valued) functions on some poset $P$, and say $\mu$ is the Mobius function of $P$. I'm studying a quantity that's a sort of "double convolution" of $f$ and $g$ ...

**3**

votes

**0**answers

126 views

### references for properties/examples of breadth in (semi)lattices

This is in some sense following up on my earlier question and the answer given by NN.
I am currently revising the paper which used the condition mentioned in my question. It was pointed out in NN's ...

**13**

votes

**6**answers

2k views

### The category of posets

I am trying to teach myself category theory and, as a begginer, I am looking for
examples that I have a hands-on experience with.
Almost every introductory text in category theory contains following ...

**6**

votes

**1**answer

355 views

### Posets of cosets and contractibility

For this question let $G$ be a group, perhaps infinite, and let $H_i$ for $i\in I$ be a (finite) family of subgroups closed under taking intersections. I am interested in the coset poset ...

**3**

votes

**1**answer

155 views

### Decomposing a poset into directed subposets

Let us say that a poset $P$ is $\mathbf{\kappa}$-directed iff every collection of fewer than $\kappa$-many elements in $P$ has an upper bound in $P$. $P$ has the $\mathbf{\kappa}$ chain condition iff ...

**4**

votes

**1**answer

293 views

### Posets of finite sequences are highly connected

I need the following result for an example in a paper I'm writing. It's easy enough to prove, but I'd prefer to just give a reference. Does anyone know one?
Fix $1 \leq k \leq n$. Define $X_{n,k}$ ...