# ineff

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bio website poisson.phc.unipi.it/~mossa location Earth age 25 member for 1 year, 11 months seen 21 mins ago profile views 220

I'm math student, in particular I'm interested in algebra, geometry, topology and category theory (especially higher dimensional category theory) and its application in mathematics.

# 260 Actions

 Dec8 comment semidirect product, split extensionFine, give me one moment I change my answer, but allow me to use my notation. Dec8 answered semidirect product, split extension Dec1 comment Reasons for coherence for bi/monoidal categoriesthanks to the answer, I realized that probably my question didn't address my doubts so I've edited it. Dec1 comment Reasons for coherence for bi/monoidal categories@ZhenLin Thanks for the comment, I completely agree with what you said, I realize my question wasn't addressing my doubt, I've edited the question, hope I've made myself more clear. Dec1 revised Reasons for coherence for bi/monoidal categoriesAdded some specifications Nov30 asked Reasons for coherence for bi/monoidal categories Nov23 comment Group actions, permutation representations and curryingThese are just some few reasons which explain why both the definitions are important, probably there are many more which I've forgotten, but I'm sure you're going to get a better understanding of these relations and their importance in particular when you're going to start to deal with ring/algebras representations and modules over said algebras, which are the ring version of group representations and actions. Nov23 comment Group actions, permutation representations and curryingActions are less group theoretic than homomorphism (at least for what's my taste), anyway in practice actions arise more naturally than representations, and they gives us a incredible beautiful and useful symbolism to deal with representations (at this point is clear that studying representations of a group is the same as studying its actions). Nov23 comment Group actions, permutation representations and currying@SJGreen you're welcome. About your last comment on the comparison between homomorphisms (but I prefer talk about representations) and actions: as you have already said they both have different advantages. Representations are good objects for theoretical reasons: they allows to deal with actions in terms of the objects of group theory (i.e. groups and group homomorphisms). This is useful because it enables to use general results about group to prove facts about actions and the other end. Nov22 answered Group actions, permutation representations and currying Nov22 revised Adjoining an element to a ringCompleted answer Nov22 comment Adjoining an element to a ringRight @YACP. Now I complete :) thanks. Nov21 comment Adjoining an element to a ringSimple: $2x - 6 = 2(x - 10) + 14$ and clearly $14 = (2x - 6) - 2(x - 10)$, so we have that $2x - 6, x - 10 \in (x - 10, 14)$ and, on the other end $14, x - 10 \in (x - 10, 2x - 6)$ so these two ideals are one contained in the other one, and so they're equal. Nov21 answered Adjoining an element to a ring Oct24 answered A collection of Isomorphic Groups Oct20 comment A model structure on $\bf Cat$Just as a comment: every functor from a category to the one object-one morphism category is a fibration but it doesn't reflect iso, generally. Oct3 comment Homotopic maps which aren't relative homotopicOk,now I get it thanks @mercio . Oct3 accepted Homotopic maps which aren't relative homotopic Oct1 accepted What is combinatorics? Oct1 comment Homotopic maps which aren't relative homotopic@mercio you're right sorry, here're the problems. in the second paragraph there's a homotopy $\bar h$ which is defined as $\bar h(x) = \dots$ instead of something like $\bar h(x,t) = \dots$, and it's also not clear (at least to me) why this map should be continuous, it doesn't seem to me that we can apply the gluing lemma.