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Very General question on the idea of categories [closed]
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First I have to say that I am a physics student, I don't know very much about mathematics but I am really intrested and fascinated by it. Anyway, my question is a very General one, and even a reference to some good text on the argument would be an appreciate answer, but here we go: I've Heard and come across the word "categories" and "Groethendick universes" and some others for some time now and tried to Read some about it; unfortunately my already mentioned lack of culture in mathematics has posed some (insurmountable) obstacles to my understanding, and it prevented me to go further Than the Basic definitions and concepts of the field. I am not asking anyone to explain me any particular concept obviously, but I was Wondering if Maybe someone could at Least explain the relevance of those ideas (the one of categories to be precise) for modern mathematics, what was the problem that made them necessary and what kind of New tools they brought to the (beautiful) field of math. I hope it is an appropriate question. Thanks in Advance!
category-theory math-history philosophy
asked Jul 23 at 23:24
user199710
212
closed as too broad by Lord Shark the Unknown, Isaac Browne, Shailesh, Claude Leibovici, Parcly Taxel Jul 24 at 8:19
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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First I have to say that I am a physics student, I don't know very much about mathematics but I am really intrested and fascinated by it. Anyway, my question is a very General one, and even a reference to some good text on the argument would be an appreciate answer, but here we go: I've Heard and come across the word "categories" and "Groethendick universes" and some others for some time now and tried to Read some about it; unfortunately my already mentioned lack of culture in mathematics has posed some (insurmountable) obstacles to my understanding, and it prevented me to go further Than the Basic definitions and concepts of the field. I am not asking anyone to explain me any particular concept obviously, but I was Wondering if Maybe someone could at Least explain the relevance of those ideas (the one of categories to be precise) for modern mathematics, what was the problem that made them necessary and what kind of New tools they brought to the (beautiful) field of math. I hope it is an appropriate question. Thanks in Advance!
category-theory math-history philosophy
asked Jul 23 at 23:24
user199710
212
closed as too broad by Lord Shark the Unknown, Isaac Browne, Shailesh, Claude Leibovici, Parcly Taxel Jul 24 at 8:19
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
2
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
First I have to say that I am a physics student, I don't know very much about mathematics but I am really intrested and fascinated by it. Anyway, my question is a very General one, and even a reference to some good text on the argument would be an appreciate answer, but here we go: I've Heard and come across the word "categories" and "Groethendick universes" and some others for some time now and tried to Read some about it; unfortunately my already mentioned lack of culture in mathematics has posed some (insurmountable) obstacles to my understanding, and it prevented me to go further Than the Basic definitions and concepts of the field. I am not asking anyone to explain me any particular concept obviously, but I was Wondering if Maybe someone could at Least explain the relevance of those ideas (the one of categories to be precise) for modern mathematics, what was the problem that made them necessary and what kind of New tools they brought to the (beautiful) field of math. I hope it is an appropriate question. Thanks in Advance!
category-theory math-history philosophy
asked Jul 23 at 23:24
user199710
212
First I have to say that I am a physics student, I don't know very much about mathematics but I am really intrested and fascinated by it. Anyway, my question is a very General one, and even a reference to some good text on the argument would be an appreciate answer, but here we go: I've Heard and come across the word "categories" and "Groethendick universes" and some others for some time now and tried to Read some about it; unfortunately my already mentioned lack of culture in mathematics has posed some (insurmountable) obstacles to my understanding, and it prevented me to go further Than the Basic definitions and concepts of the field. I am not asking anyone to explain me any particular concept obviously, but I was Wondering if Maybe someone could at Least explain the relevance of those ideas (the one of categories to be precise) for modern mathematics, what was the problem that made them necessary and what kind of New tools they brought to the (beautiful) field of math. I hope it is an appropriate question. Thanks in Advance!
category-theory math-history philosophy
asked Jul 23 at 23:24
user199710
212
asked Jul 23 at 23:24
user199710
212
asked Jul 23 at 23:24
user199710
212
asked Jul 23 at 23:24
user199710
212
212
closed as too broad by Lord Shark the Unknown, Isaac Browne, Shailesh, Claude Leibovici, Parcly Taxel Jul 24 at 8:19
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by Lord Shark the Unknown, Isaac Browne, Shailesh, Claude Leibovici, Parcly Taxel Jul 24 at 8:19
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
2
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38
add a comment |Â
Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
2
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38
Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
2
2
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38
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Explanation will come, or the thread will be closed. As a general piece of advice, let me only say this. Google: "good abstract algebra book with a lot of exercises". Study the book to the best of your abilities. Google "good general topology book with a lot of exercises". Study the book to the best of your abilities. Same with a "good algebraic topology book with a lot of exercises". Then open any book on category theory (e.g. this one). Things will be way clearer. Re-read the algebra book. Re-read the topology book. Repeat the cycle. Good luck!
– Fosco Loregian
Jul 23 at 23:45
2
Maybe one Day I Will do it, but for now unfortunately my studies don't leave much free time to concentrate on such an High Level target, otherwise I'd be already doing that! Thank you for your advice!
– user199710
Jul 23 at 23:49
Thank you Also for the pdf!
– user199710
Jul 23 at 23:54
The origin of categories is somewhere around module theory, exact sequences, projective/injective objects, and especially the diagrams in 'diagram chasing techniques' motivated it. They have probably already drawn these for a while when realized exactly what and how to extract from the picture to arrive to pure category theory. Grothendieck universes are just a tool to overcome seemingly paradoxical setups when we want to talk about the category of all sets / modules / categories / whatever
– Berci
Jul 24 at 22:38