# Questions tagged [diagram-chasing]

For questions about proofs using equivalent map compositions in commutative diagrams in homological algebra, or in category theory in general.

52 questions
334 views

### Category theorists: would you use a software tool for diagramming / chasing?

Update: Source Code Repository Screenshots: Now the users can edit the default colors of arrows, nodes etc. using the ColorEditor: Users can draw diagrams and store them into a Graph Database (...
15 views

837 views

### Equalizers by pullbacks and products

I'm trying to solve exercise 5.6 in Steve Awodey's "Category Theory": Show that a category with pull-backs and products has equalizers as follows: given arrows $f, g: A \to B$, take the pullback ...
35 views

### Vertical and top arrows??

Here in her short note in the middle of the page 1, Emily Riehl says ...with the top two vertical arrows ... I just wonder how vertical arrows can be top or bottom. I would say that vertical arrows ...
93 views

### Why is this universal map in a proof of the co-Yoneda lemma actually natural?

I'm attempting to prove that every presheaf is a canonical colimit of representable presheaves by constructing a limiting cocone directly (I'm aware that there are more elegant proofs, but this is ...
109 views

### How would one solve Weibel 1.3.1 in a general Abelian category?

Working through Weibel's Introduction to Homological Algebra, I am frequently unsure when it is acceptable to prove results using diagram-chasing and elements, and when Weibel has in mind a category-...
59 views

### A question about the functoriality of the module of derivations on the category of algebras

Assume that all rings are commutative with identity. Let $k$ be a fixed ring with $k$-algebras $\varphi: k \rightarrow R$ and $\tau: k \rightarrow A$. Let $\tau' : R \rightarrow B$ define an $R$-...
57 views

202 views

### Proving the (Strong) Four Lemma using the Snake Lemma

$\DeclareMathOperator{\im}{im} \DeclareMathOperator{\coker}{coker} \require{AMScd}$ The usual formulation of the Strong Four Lemma is: given the diagram below, if the rows are exact, $\alpha$ is epic, ...
91 views

### The Existence of a Natural Isomorphism Confirming the Existence of a Limit, as a Commutativity Diagram

I am reading Category Theory for Programmers and I am having some trouble in Part 2, Chapter 2: Limits and Colimits. The author writes: Now that we have two functors, we can talk about natural ...