In what categories does the “classical” notion of function make sense?
I'm new to category theory, and I often struggle to choose the right level of abstraction when working with categories. I also found that many textbooks are rather inconsistent in their conventions with regards to the terminology (eg. they often interchangeably use terms like epimorphism and surjection, etc). So I wondered what's a minimal set of requirements on a category so that it makes sense to say that morphism are functions? How about Abelian categories?
functions category-theory
asked 4 hours ago
gen
4232521
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I'm new to category theory, and I often struggle to choose the right level of abstraction when working with categories. I also found that many textbooks are rather inconsistent in their conventions with regards to the terminology (eg. they often interchangeably use terms like epimorphism and surjection, etc). So I wondered what's a minimal set of requirements on a category so that it makes sense to say that morphism are functions? How about Abelian categories?
functions category-theory
asked 4 hours ago
gen
4232521
add a comment |
I'm new to category theory, and I often struggle to choose the right level of abstraction when working with categories. I also found that many textbooks are rather inconsistent in their conventions with regards to the terminology (eg. they often interchangeably use terms like epimorphism and surjection, etc). So I wondered what's a minimal set of requirements on a category so that it makes sense to say that morphism are functions? How about Abelian categories?
functions category-theory
asked 4 hours ago
gen
4232521
I'm new to category theory, and I often struggle to choose the right level of abstraction when working with categories. I also found that many textbooks are rather inconsistent in their conventions with regards to the terminology (eg. they often interchangeably use terms like epimorphism and surjection, etc). So I wondered what's a minimal set of requirements on a category so that it makes sense to say that morphism are functions? How about Abelian categories?
functions category-theory
functions category-theory
asked 4 hours ago
gen
4232521
asked 4 hours ago
gen
4232521
asked 4 hours ago
gen
4232521
asked 4 hours ago
gen
4232521
asked 4 hours ago
gen
4232521
4232521
add a comment |
add a comment |
1 Answer
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The notion you are looking for is probably that of a concrete category. A concrete category is a category that is embedded in the category of sets; thus its objects are associated with actual sets, and its morphisms are associated with actual functions.
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
The notion you are looking for is probably that of a concrete category. A concrete category is a category that is embedded in the category of sets; thus its objects are associated with actual sets, and its morphisms are associated with actual functions.
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
add a comment |
The notion you are looking for is probably that of a concrete category. A concrete category is a category that is embedded in the category of sets; thus its objects are associated with actual sets, and its morphisms are associated with actual functions.
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
add a comment |
The notion you are looking for is probably that of a concrete category. A concrete category is a category that is embedded in the category of sets; thus its objects are associated with actual sets, and its morphisms are associated with actual functions.
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
The notion you are looking for is probably that of a concrete category. A concrete category is a category that is embedded in the category of sets; thus its objects are associated with actual sets, and its morphisms are associated with actual functions.
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
answered 3 hours ago
Pierre-Guy Plamondon
8,50011638
8,50011638
add a comment |
add a comment |
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