Timeline for Is Grassman algebra an F-algebra? [closed]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2013 at 13:52 | history | closed |
David White Andrés E. Caicedo Willie Wong Daniel Moskovich Noah Stein |
Needs details or clarity | |
| Aug 5, 2013 at 1:28 | answer | added | Qiaochu Yuan | timeline score: 2 | |
| Aug 4, 2013 at 18:22 | review | Close votes | |||
| Aug 5, 2013 at 13:52 | |||||
| Aug 4, 2013 at 17:41 | history | edited | user9072 |
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| Jun 25, 2013 at 3:02 | review | First posts | |||
| Jun 26, 2013 at 4:29 | |||||
| Jun 1, 2013 at 19:33 | comment | added | Bartosz Milewski | Sorry, I'm new to mathoverflow and I'm not a mathematician. I know about Grassman algebras from physics (supersymmetry) and about F-algebras from programming (Haskell), so I'm asking this question from a somewhat narrow point of view. Indeed, I was thinking of vector spaces and the wedge product. Is there a triple (endofunctor F, object A, and morphism F(A)->A) that can be used to define an exterior algebra? Or would Grassman algebra be the initial algebra for such a triple? I'm looking for some intuitions. | |
| Jun 1, 2013 at 5:57 | comment | added | Theo Johnson-Freyd | Presumably the question is something like: On the category of vector spaces, is there an endofunctor $F$ whose algebras are precisely the Grassmann (=exterior) algebras? I say "something like" because of course one could replace "vector spaces" by some other category, or ask that $F$ be a monad, or so on. (The latter does not seem to be the common usage en.wikipedia.org/wiki/F-algebra.) Bartosz, please read mathoverflow.net/howtoask, and also look over other MathOverflow questions, and revise your question. | |
| Jun 1, 2013 at 2:06 | comment | added | Todd Trimble | This question needs to be tightened considerably. The answer to the title question is "yes, of course": any object of any category is an algebra over the identity endofunctor; typically objects can be realized in many ways as algebras over endofunctors $F$ for various $F$. But if you provided more context, there's a good chance you'll get more satisfying answers. | |
| Jun 1, 2013 at 0:42 | history | asked | Bartosz Milewski | CC BY-SA 3.0 |