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rename fields to align
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s3midetnov committed Aug 10, 2024
1 parent 381e414 commit acfc723
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Showing 3 changed files with 11 additions and 11 deletions.
8 changes: 4 additions & 4 deletions src/Algebra/Group/Representation/Category.ard
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Expand Up @@ -58,8 +58,8 @@
| ** (g : G) (e : KerLModule f) => (g A.** e.1, rewrite (f.func-**, e.2, B.g**-zro) idp)
| **-assoc {_ _ : G} {_ : KerLModule f} => exts A.**-assoc
| id-action => exts A.id-action
| lin => exts A.lin
| lin-*c => exts A.lin-*c
| **-ldistr => exts A.**-ldistr
| **-*c => exts A.**-*c


\func KerLRepresHom {R : Ring} {G : Group} {A B : LRepres R G} (f : InterwiningMap A B) : InterwiningMap (KerLRepres f) A \cowith
Expand All @@ -71,8 +71,8 @@
| ** (g : G) (e : ImageLModule f) => (g B.** e.1, TruncP.map e.2 \lam s => (g A.** s.1, func-** *> pmap (g B.**) s.2))
| **-assoc => ext B.**-assoc
| id-action => ext B.id-action
| lin => ext B.lin
| lin-*c => ext B.lin-*c
| **-ldistr => ext B.**-ldistr
| **-*c => ext B.**-*c



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Expand Up @@ -23,8 +23,8 @@
| LModule => Module
| ** g f j => f (inverse g X.** j)
| **-assoc => ext (\lam _ => rewrite (X.**-assoc, inverse_prod) idp)
| lin => idp
| lin-*c => ext (\lam _ => idp)
| **-ldistr => idp
| **-*c => ext (\lam _ => idp)
| id-action => ext (\lam _ => rewrite (G.inverse_ide, X.id-action) idp)
\where{
\func inverse_prod {m n : G} : inverse (m * n) = inverse n * inverse m =>
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10 changes: 5 additions & 5 deletions src/Algebra/Group/Representation/Representation.ard
Original file line number Diff line number Diff line change
Expand Up @@ -32,10 +32,10 @@
-- also : https://www.maths.dur.ac.uk/users/jack.g.shotton/repthy/index.html

\class LinRepres \extends LModule, GroupAction {
| lin {g : G} {e e' : E} : g ** (e + e') = g ** e + g ** e'
| lin-*c {g : G} {e : E} {c : R} : g ** (c *c e) = c *c (g ** e)
| **-ldistr {g : G} {e e' : E} : g ** (e + e') = g ** e + g ** e'
| **-*c {g : G} {e : E} {c : R} : g ** (c *c e) = c *c (g ** e)

\func g**-zro {g : G} : g ** 0 = 0 => rewrite (inv *c_zro-right, lin-*c, *c_zro-left, *c_zro-left) idp
\func g**-zro {g : G} : g ** 0 = 0 => rewrite (inv *c_zro-right, **-*c, *c_zro-left, *c_zro-left) idp
}

\func LRepres (R : Ring)(G : Group) : \Type => LinRepres {| R => R | G => G}
Expand All @@ -44,5 +44,5 @@
\func TrivialAction {R : Ring}(E : LModule R)(G : Group) : LRepres R G \cowith
| LModule => E
| GroupAction => trivialAction G E
| lin-*c => idp
| lin => idp
| **-*c => idp
| **-ldistr => idp

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