For example, when dealing with sheaves or simplicial sets, usually a diagram of the shape $$\begin{array}{c} \bullet & \rightrightarrows & \bullet \\ \downarrow && \downarrow \\ \bullet & \rightrightarrows & \bullet \end{array}$$ is called commutative if the two squares which consist of the two upper resp. lower horizontal morphisms are ...

commutative diagram. Ask Question Asked 11 years, 11 months ago. Modified 11 years, 11 months ago. Viewed ...

2014年12月17日 · Hi and welcome, you could also check out Creating triangle commutative diagram with tikz-cd or Commutative Diagrams or Commutative Diagrams and TikZ or How to draw a single commutative diagram with double-ended arrow? –

If you haven't run into a problem where it seems like using a commutative diagram would help you express some idea, then I wouldn't try to force the issue. Wait until you actually feel the need. In this particular case, the first commutative diagram you wrote down expresses the naturality of the exterior derivative.

2021年10月5日 · Here is the commutative diagram for the Fundamental Theorem of Homomorphisms, in case a particular diagram is needed for the answer. (I've only encountered commutative diagrams in the context of abstract algebra, I am not familiar with category theory or uses of this diagram outside of abstract algebra).

2020年8月15日 · Definition 3.27: A diagram in a 2-category is called 2-commutative, if its 1- morphisms commute up to given 2-isomorphisms and these 2-isomorphisms commute in the induced diagram taking 1-morphisms (and their compositions) as vertices.

2021年3月7日 · $\begingroup$ "a diagram commutes means that between any two objects in the diagram, there is a unique morphism." -- To my understanding, this isn't even part of the standard definition of a (commutative) diagram. To answer your second question, at least in my experience we rarely have the same object twice in a diagram.

2021年7月1日 · The short five lemma says that if the diagram is commutative and $\alpha$ and $\gamma$ are modules ...

2012年7月5日 · What is the meaning of a commutative diagram in mathematics? For example, if a map translate an object, then rotate it around the origin and then translate it again, is this a commutative diagram?

Commutative diagram with exact sequences as columns and rows. 0. Elementary Group Homomorphisms. 1. Are ...