6
votes
1answer
192 views

Terminology question for poset maps

Is there a standard name for order-preserving maps $f\colon P\to Q$ of posets with the property that the image of a lower set is a lower set, or equivalently if $q\leq f(p)$ then there exists $p'\leq ...
13
votes
6answers
1k 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 ...
2
votes
1answer
261 views

What are $n$-poset?

Yesterday I was wandering for the $n$-lab and I've found the definition of $n$-poset. Following this post it seems that a $n$-poset should be a $(n,n+1)$-category. Now an $(n,r)$-category should be a ...
2
votes
0answers
119 views

non-degenarete tools to calculate a derived functor on a model category which is a poset?

Are there theorems (esp. computational tools) on model categories which survive and do not trivialise when its underlying category is a (quasi-)poset ? Are there tools that may help to calculate ...
4
votes
4answers
752 views

Category = Groupoid x Poset?

Is it possible to split a given category $C$ up into its groupoid of isomorphisms and a category that resembles a poset? "Splitting up" should be that $C$ can be expressed as some kind of extension ...