Questions tagged [diagram-chasing]

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

Diagram chasing is a method for proving statements using equivalent map compositions in commutative diagrams, thereby using properties of the diagram such as injective or surjective maps, or exact sequences. Mostly used in homological algebra and category theory. Examples include the five lemma, the snake lemma and the nine lemma.

See also Diagram Chasing at MathWorld.

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what are the steps i have to take to find the sets that represent the red colored in the diagram?

i tried using the notation to make it all separate and then see if i can put all the solution i get from each a,b, c together but i couldn't understand what i am doing wrong. if anyone could help with understanding this will be great, I have midterm…
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pushout with zero upper map

If \begin{array}{ccC} A &\xrightarrow {0} & B\\ \downarrow & &\downarrow \\ C & \xrightarrow{g} & D \end{array} is a pushout. is $g$ zero map?