Structures · Algebra
Rack
A rack is an automorphic set (a set with an action on itself by
bijections) that is self-distributive. It is a shelf such that each
element's action is invertible.
The notations x ◃ y and x ◃⁻¹ y denote the action and the
inverse action, respectively, and they are right associative.
- Defined in
- Mathlib.Algebra.Quandle
- Shape
- One type argument · adds invAct, left_inv, right_inv
Extends1
Extended by1
Concrete types that are instances1
- MulOpposite
How is a type an instance?
Loading the hierarchy index…
Assumed by64
- Rack.invAct
- Rack.left_cancel
- Rack.act'
- Rack.right_inv
- Rack.self_act_act_eq
- Rack.EnvelGroup
- Rack.toEnvelGroup
- Rack.toEnvelGroup.map
- Rack.PreEnvelGroupRel'.rel
- Rack.PreEnvelGroupRel'.brecOn
- Rack.toEnvelGroup.mapAux
- Rack.self_act_eq_iff_eq
- Rack.left_inv
- Rack.self_act_invAct_eq
- Rack.envelAction
- Rack.act_invAct_eq
- Rack.PreEnvelGroupRel'.brecOn.go
- Rack.PreEnvelGroupRel'.below
- Rack.IsInvolutory
- Rack.IsAbelian
- Rack.involutory_invAct_eq_act
- Rack.toEnvelGroup.univ_uniq
- Rack.PreEnvelGroupRel'.trans.elim
- Rack.PreEnvelGroupRel.symm
- Rack.PreEnvelGroupRel'.one_mul.elim
- Rack.invAct_act_eq
- Rack.selfApplyEquiv
- Rack.PreEnvelGroupRel'.assoc.elim
- Rack.PreEnvelGroupRel'.refl.elim
- Rack.act'_symm_apply
- Rack.invAct_apply
- Rack.toEnvelGroup.mapAux.eq_def
- Rack.PreEnvelGroupRel'.brecOn.eq
- Rack.PreEnvelGroupRel.refl
- Rack.self_invAct_eq_iff_eq
- Rack.envelAction_prop
- Rack.left_cancel_inv
- Rack.PreEnvelGroupRel'.ctorElim
- Rack.self_distrib_inv
- Rack.oppositeRack
- Rack.ad_conj
- Rack.op_invAct_op_eq
- Rack.instGroupEnvelGroup
- Rack.act'_apply
- Rack.op_act_op_eq
- Rack.self_invAct_invAct_eq
- Rack.self_invAct_act_eq
- Rack.PreEnvelGroup.setoid
- Rack.PreEnvelGroupRel'.act_incl.elim
- Rack.PreEnvelGroupRel.trans