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Apr
17
comment Are $R=K[a,b,c,d]/(ad-bc, a^2c-b^3, bd^2-c^3, ac^2-b^2d)$ and $K[x^4,x^3y,xy^3,y^4]$ isomorphic?
Great answer! A couple of questions: i) shouldn't it be $I = (a-x^4, \dots )$? ii) is the variable $z$ really needed?
Apr
14
comment Incidence variety fo Grassmmanians
I don't think this is a morphism of varieties, otherwise you could prove, adapting the map, that every subset of a variety should be closed.
Mar
22
accepted Reflexivity of equality in sequent calculus
Mar
10
revised Reflexivity of equality in sequent calculus
Edit: cut rule
Mar
10
asked Reflexivity of equality in sequent calculus
Jan
16
awarded  Yearling
Oct
30
accepted Ring and $A$-module, but not $A$-algebra
Oct
30
asked Ring and $A$-module, but not $A$-algebra
Jun
29
comment A little confusion about extensions $E(-,-)$ and $\mathrm{Ext}(-,-)$
It is rather a feeling and I may mistake, but I suppose what changes is the projection $\pi_i \colon \mathbb Z \to \mathbb Z/(p)$.
Jun
29
comment Developing category theory inside ETCS
Universe in a topos. Note that this formulation is stricly relating to Zhen Lin's answer.
Jun
29
comment Developing category theory inside ETCS
In Lawvere's world, $\mathcal C_i, i=1, 2$ live in ETCC. Actually, you need less than all ETCC to formalize ETCS. Take a curious look at this page on nlab. As you can see, axioms are really easy.
Jun
29
answered Developing category theory inside ETCS
Jun
4
awarded  Critic
Jun
4
awarded  Excavator
Jun
4
revised Algebraic Intuition for Homological Algebra and Applications to More Elementary Algebra
Typo edited
Jun
4
suggested suggested edit on Algebraic Intuition for Homological Algebra and Applications to More Elementary Algebra
Jun
3
comment Split-Lemma for chain complexes
You are welcome. The one by Andrea Blass is also very cool and minimal.
Jun
3
answered Split-Lemma for chain complexes
Jun
3
comment Split-Lemma for chain complexes
Ok, my bad too: obviously, the differential on $C_k$ is $d^{C_\bullet}_{k+1}\colon C_{k+1} \to C_k$. Actually, I don't understand the last two lines of your counter-example. What you get is that $\text{Im}(s_{k+1})\subseteq \text{Ker}(d^{B_\bullet}_{k+1})$. How do you conclude that $s_{k+1}$ is not injective or, worse, is the zero morphism?
Jun
3
comment Split-Lemma for chain complexes
Wait. Are you using homological or cohomological notation? The subscript indexes are typical of homological notation. But what you have just written doesn't make sense that way.