Questions tagged [equalisers]
7 questions
4
votes
5 answers
Category where not every mono is regular
I'm looking for a category with the titular property. Since $f : A \to B$ is supposed to be mono, the desired factorisation is automatically unique (correct?). Thus, I would need to find a category in which the factorisation does not exist, i.e.,…
Jos van Nieuwman
- 2,142
2
votes
2 answers
Equaliser of $f$ and $g$ is an isomorphism iff $f = g$
I've proven that, given an equaliser diagram where the equaliser map $e : E \to X$ is an isomorphism, the equalised maps $f, g : X \to Y$ say, must be equal.
Conversely, if we assume the equalised maps $f$ and $g$ are already equal, I can find a…
Jos van Nieuwman
- 2,142
1
vote
1 answer
Questions about the definition of normal category and wording of an exercise.
The following is taken from 'Theory of Categories" by Barry Mitchell
$\color{Green}{Background:}$
$\textbf{(1) Definition:}$
If $\alpha;A'\to A$ is a monomorphism, we shall call $A'$ a $\textbf{subobject}$ of $A,$ and we shall refer to $\alpha$ as…
Seth
- 4,043
1
vote
1 answer
Need help with finding a counterexample to: if $2^h=coeq(2^{q_1}, 2^{q_2}).$ then $h=eq(q_1,q_2)$
The following question is taken from Arrows, Structures and Functors the categorical imperative by Arbib and Manes
Notations: Let $2^A$ denote the $\textit{power set}$ of all subsets of $A.$ Given $f:A\rightarrow B$, define $2^f:2^b\rightarrow…
Seth
- 4,043
0
votes
0 answers
What must my function be divided by to equal my other function?
Here is a problem I have struggled on for hours. Hopefully it shouldn't be too difficult for someone more skilled at math.
Here I have my first function:
$$R_{oM} = \frac{p R_t^2 + 2 R_t R_n^2}{2 R_n^2 + p (1+ 3 c_M r_m) R_t}$$
All of the variables…
Electric-Gecko
- 151
0
votes
1 answer
Is every split mono regular?
Let $f : A \to B$ be a split mono: $(\exists g : B \to A)(g \circ f = \text{id}_A)$.
(It it clear that $f$ is in particular a monomorphim.) I want to show that it is regular, i.e., there is an object $C$ and parallel arrows $k, l : B \to C$ such…
Jos van Nieuwman
- 2,142
0
votes
1 answer
In $\textbf{Set}$, does every monomorphism fit into *a* or *any* equaliser diagram?
The question is posed as 'a' diagram. In this case, given a mono $f : X \to Y$ and parallel arrows $g, h : Y \to Z$, we would have the freedom to choose $Z = Y$ and $h = \text{id}_Y$. This would make things a lot easier, because then we would have…
Jos van Nieuwman
- 2,142