Take two posets $A, B$ (partially ordered sets). Now consider these posets to be categories $Cat(A), Cat(B)$ respectively. Consider a map from $A$ to $B$, $f: A \rightarrow B$. This can be seen as ...
The following appears naturally in a certain context: Let $P$ be a graded partially ordered set. Let $M$ be the subset of minimal elements of $P$. Define subsets $E_i$ inductively as follows: First, ...
What is known about the category that has small categories as objects and adjunctions as morphisms? Obviously, it has neither terminal nor initial objects. But what about other kinds of limits? Are ...
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 ...
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 ...
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 ...
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 ...
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 ...