In what categories does the “classical” notion of function make sense?












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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?






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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







    share|cite|improve this question

























      3












      3








      3







      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







      share|cite|improve this question













      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






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      gen

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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.






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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.






            share|cite|improve this answer


























              6














              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.






              share|cite|improve this answer
























                6












                6








                6






                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.






                share|cite|improve this answer












                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.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 2 hours ago









                Pierre-Guy Plamondon

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