caa a22 4500 388108916 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500031036 doi S0308210500031036 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500031036 Leech Jonathan Department of Mathematics, Westmont College, 955 La Paz Road, Santa Barbara, CA 93108-1099, USA (leech@westmont.edu) Symmetric groupoids, free categories and E*-unitary inverse monoids [Elektronische Daten] [Jonathan Leech] Symmetric groupoids which classify the monomorphism contexts of objects in arbitrary categories are studied, along with their connections to symmetric inverse monoids and symmetric inverse algebras. Particular attention is given to symmetric groupoids of objects in free categories and to the inverse algebras induced from them by 0-closure. These graph algebras generalize both the class of polycyclic semigroups and the class of combinatorial ω-semigroups with adjoined zeros. Since all such algebras are E*-unitary, an analogue of McAlister's theory of.E-unitary inverse monoids is developed for a special class of E*-unitary inverse monoids and then illustrated on the class of graph algebras. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 959-984 0308-2105 129:5<959 1999 129 PRM https://doi.org/10.1017/S0308210500031036 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500031036 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Leech Jonathan Department of Mathematics, Westmont College, 955 La Paz Road, Santa Barbara, CA 93108-1099, USA (leech@westmont.edu) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 959-984 0308-2105 129:5<959 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge