Four Functors. The 'ancestor' of Mundici's equivalence between unital commutative l-groups and MV algebras...

— —

Afrodita Iorgulescu

Four Functors. The 'ancestor' of Mundici's equivalence between unital commutative l-groups and MV algebras

Afrodita Iorgulescu

$52.95 $45.29

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

College Publications
01 October 2025

Mathematical logic; Algebra

Summary
Details

Daniele Mundici has proved in 1986 that the category of lattice-ordered commutative groups with strong unit (or unital commutative l-groups, for short) is equivalent to the category of MV algebras, by proving the existance of the quasi-inverse functors Gamma and Xi. He has made the proof in one step, but the proof can be made in two steps, as it is sketched in this book, by introducing the intermediary category of positive-unital commutative l-groups and four functors.

Marco Abbadini has presented in 2021 his equivalence à la Mundici for commutative l-monoids, in two steps, with four functors.

Afrodita Iorgulescu has introduced and studied in 2020 a new commutative framework, centered on m-BCK algebras, containing the commutative groups and the MV algebras. Hence, she has had sufficient background material to generalize Mundici's equivalence, to fi nd its 'ancestor'. The role of unital commutative l-groups is played by the strong mo-ME structures, the role of positive unital commutative l-groups is played by the strong mo-ME positive cones, and the role of MV algebras is played by the XY algebras, all belonging to this new framework. She presents in this book this 'ancestor', in two steps, with four functors: the category of strong mo-ME structures is not equivalent to the category of strong mo-ME positive cones (step 1), but

the category of strong mo-ME positive cones is equivalent to the category of XY algebras (step 2).

Abbadini's results and the wonderful instrument which is Prover9-Mace4 were of major help in writing this book.

By: Afrodita Iorgulescu
Imprint: College Publications
Dimensions: Height: 234mm, Width: 156mm, Spine: 18mm
Weight: 467g
ISBN: 9781848904965
ISBN 10: 1848904967
Pages: 332
Publication Date: 01 October 2025
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

PRIZES to win! PROMOTIONS

Four Functors. The 'ancestor' of Mundici's equivalence between unital commutative l-groups and MV algebras

Afrodita Iorgulescu

$52.95 $45.29

Paperback

See Also

Contact Abbeys

Contact Galaxy

Contact Language

Contact Us

About ABBEY'S