fix left module namespace
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3 changed files with 8 additions and 11 deletions
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@ -8,9 +8,7 @@ Modules prod vector spaces over a ring.
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(We use "left_module," which is more precise, because "module" is a keyword.)
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-/
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import algebra.field ..move_to_lib
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open is_trunc pointed function sigma eq
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namespace algebra
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open is_trunc pointed function sigma eq algebra
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structure has_scalar [class] (F V : Type) :=
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(smul : F → V → V)
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@ -19,6 +17,8 @@ infixl ` • `:73 := has_scalar.smul
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/- modules over a ring -/
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namespace left_module
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structure left_module (R M : Type) [ringR : ring R] extends has_scalar R M, ab_group M renaming
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mul→add mul_assoc→add_assoc one→zero one_mul→zero_add mul_one→add_zero inv→neg
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mul_left_inv→add_left_inv mul_comm→add_comm :=
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@ -155,7 +155,7 @@ pointed.mk zero
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definition pSet_of_LeftModule [coercion] {R : Ring} (M : LeftModule R) : Set* :=
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pSet.mk' (LeftModule.carrier M)
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namespace left_module
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section
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variable {R : Ring}
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structure homomorphism (M₁ M₂ : LeftModule R) : Type :=
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@ -219,6 +219,6 @@ namespace left_module
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end
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end
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end left_module
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end
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end algebra
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end left_module
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@ -6,7 +6,7 @@ open eq pointed sigma fiber equiv is_equiv sigma.ops is_trunc nat trunc
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open algebra function
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open chain_complex
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open succ_str
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open algebra.left_module
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open left_module
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structure module_chain_complex (R : Ring) (N : succ_str) : Type :=
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(mod : N → LeftModule R)
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@ -4,10 +4,7 @@ Author: Jeremy Avigad
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import .module_chain_complex
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open eq pointed sigma fiber equiv is_equiv sigma.ops is_trunc nat trunc
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open algebra function succ_str
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-- TODO: reconcile these
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open algebra.left_module -- name in left_module
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open left_module -- namespace in hott library
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open left_module
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section short_five
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variable {R : Ring}
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