## Antimorphic Action: Categories of Algebraic Structures with Involutions Or Anti-endomorphisms |

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### Contents

K Abstract Expansions l | 1 |

Concrete Expansions ll | 14 |

The Involution Theorem | 48 |

Copyright | |

8 other sections not shown

### Common terms and phrases

a,b e anti-identity antihomomorphism antimorphisms AssAlg associative pairs BD-algebra BoolAlg Boolean algebra bounded distributive lattices bounded lattices cogenerator commutative completely liftable concrete expansion congruence extension property conjugate contravariant coproduct coreflective subvariety Cornish and Fowler Corollary defined denoted distributive lattices dual duality endomorphism equivalence expandable concrete category expandable functor finite forgetful functor free algebra free products front adjunction full subcategory given Grpd Hence homomorphism i e Ob(JJ identity-element induced expansion involution Jacobson Jordan algebra left adjoint Lemma M-compatible Math monoid morphisms non-associative ring non-trivial notation Ob(IJ Ob(X Ockham algebras one-to-one polar algebras Pr(A preserves antimorphisms prime ideal Proof quasimetric space right adjoint satisfies the identities Section skew lattices standard expansion subalgebra subset subvariety Suppose Theorem Todc topological space trivial expansion unique variety vector spaces X-algebra X-morphism