Skip to main content
MathOverflow

Return to Question

fixed typo
Source Link
Fred Rohrer
Fred Rohrer
  • 6.7k
  • 1
  • 27
  • 44

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$$Lex(\mathcal{C},\mathcal{Ab})$ is cocomplete and has an injective Cogeneratorcogenerator?

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{C},\mathcal{Ab})$ is cocomplete and has an injective cogenerator?

edited body
Source Link
Harald
Harald
  • 21
  • 2

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{A}, \mathcal{B})$$Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{A}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?

Source Link
Harald
Harald
  • 21
  • 2

Why are the left exact functors from an abelian category to abelian groups cocomplete and have a injective generator?

Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{A}, \mathcal{B})$ the category of left exact functors between abelian categories.

What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?