We prove that in the category of firm acts over a firm semigroup monomorphisms co-incide with regular monomorphisms and we give an example of a non-injective monomorphism in this category. We also study conditions under which monomorphisms are injective and we prove that the lattice of subobjects of a firm act over a firm semigroup is isomorphic to the lattice unitary subacts of that act.
Borceux, F., Handbook of Categorical Algebra 1: Basic Category Theory, Cambridge University Press, Cambridge, 1994.
Borceux, F., Handbook of Categorical Algebra 1: Basic Category Theory, Cambridge University Press, Cambridge, 1994.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
H-1051 Budapest, Hungary, Széchenyi István tér 9.
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