Graded Ring Category vs Ring Category
up vote
0
down vote
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I know that in Ring Category we have:
-Objects: Rings.
-Arrows: Ring homomorphisms.
I do not know which are the objects and arrows in Graded Ring Category.
In general, which is the definition of Graded Ring Category?
P.S. I need it in order to see why it makes a difference to take inverse limit in this two categories. (I am working in symmetric functions vs symmetric polynomials. Do not see the difference between this two concepts.)
abstract-algebra category-theory symmetric-polynomials symmetric-functions
asked Nov 22 at 15:01
idriskameni
608
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up vote
0
down vote
favorite
I know that in Ring Category we have:
-Objects: Rings.
-Arrows: Ring homomorphisms.
I do not know which are the objects and arrows in Graded Ring Category.
In general, which is the definition of Graded Ring Category?
P.S. I need it in order to see why it makes a difference to take inverse limit in this two categories. (I am working in symmetric functions vs symmetric polynomials. Do not see the difference between this two concepts.)
abstract-algebra category-theory symmetric-polynomials symmetric-functions
asked Nov 22 at 15:01
idriskameni
608
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I know that in Ring Category we have:
-Objects: Rings.
-Arrows: Ring homomorphisms.
I do not know which are the objects and arrows in Graded Ring Category.
In general, which is the definition of Graded Ring Category?
P.S. I need it in order to see why it makes a difference to take inverse limit in this two categories. (I am working in symmetric functions vs symmetric polynomials. Do not see the difference between this two concepts.)
abstract-algebra category-theory symmetric-polynomials symmetric-functions
asked Nov 22 at 15:01
idriskameni
608
I know that in Ring Category we have:
-Objects: Rings.
-Arrows: Ring homomorphisms.
I do not know which are the objects and arrows in Graded Ring Category.
In general, which is the definition of Graded Ring Category?
P.S. I need it in order to see why it makes a difference to take inverse limit in this two categories. (I am working in symmetric functions vs symmetric polynomials. Do not see the difference between this two concepts.)
abstract-algebra category-theory symmetric-polynomials symmetric-functions
abstract-algebra category-theory symmetric-polynomials symmetric-functions
asked Nov 22 at 15:01
idriskameni
608
asked Nov 22 at 15:01
idriskameni
608
asked Nov 22 at 15:01
idriskameni
608
asked Nov 22 at 15:01
idriskameni
608
asked Nov 22 at 15:01
idriskameni
608
608
add a comment |
add a comment |
1 Answer
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A graded ring can mean a few different things, but it's usually a sequence of abelian groups $R_i$ together with multiplication maps $R_iotimes R_jto R_{i+j}$ satisfying associativity, with a unit element $1in R_0$. A morphism of graded rings is a sequence of abelian group maps respecting multiplication and unit.
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
A graded ring can mean a few different things, but it's usually a sequence of abelian groups $R_i$ together with multiplication maps $R_iotimes R_jto R_{i+j}$ satisfying associativity, with a unit element $1in R_0$. A morphism of graded rings is a sequence of abelian group maps respecting multiplication and unit.
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
add a comment |
up vote
3
down vote
accepted
A graded ring can mean a few different things, but it's usually a sequence of abelian groups $R_i$ together with multiplication maps $R_iotimes R_jto R_{i+j}$ satisfying associativity, with a unit element $1in R_0$. A morphism of graded rings is a sequence of abelian group maps respecting multiplication and unit.
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
A graded ring can mean a few different things, but it's usually a sequence of abelian groups $R_i$ together with multiplication maps $R_iotimes R_jto R_{i+j}$ satisfying associativity, with a unit element $1in R_0$. A morphism of graded rings is a sequence of abelian group maps respecting multiplication and unit.
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
A graded ring can mean a few different things, but it's usually a sequence of abelian groups $R_i$ together with multiplication maps $R_iotimes R_jto R_{i+j}$ satisfying associativity, with a unit element $1in R_0$. A morphism of graded rings is a sequence of abelian group maps respecting multiplication and unit.
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
answered Nov 22 at 16:26
Kevin Carlson
32.3k23270
32.3k23270
add a comment |
add a comment |
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