[1] Adámek, J. and Rosický, J., "Locally Presentable and Accessible Categories", Cambridge University Press, 1994.
[2] Adámek, J. and Rosický, J., On pure quotients and pure subobjects, Czechoslovak Math. J. 54(129) (2004), 623-636.
[3] Borceux, F., "Handbook of Categorical Algebra 1: Basic Category Theory", Cambridge University Press, 1994.
[4] Borceux, F. and Rosický, J., Purity in algebra, Algebra Universalis 56 (2007), 17-35.
[5] Bulman-Fleming, S., Pullback-flat acts are strongly flat, Canad. Math. Bull. 34 (1991), 456-461.
[6] Bulman-Fleming, S. and Laan, V., Lazard’s Theorem for S-posets, Math. Nachr. 278 (2005), 1743-1755.
[7] Bulman-Fleming, S. and Laan, V., Tensor products and preservation of limits, for acts over monoids, Semigroup Forum 63 (2001), 161-179.
[8] Bulman-Fleming, S. and McDowell, K., Absolutely flat semigroups, Pacific J. Math. 107 (1983), 319-333.
[9] Chen, Y., Projective S-acts and exact functors, Algebra Colloq. 7 (2000), 113-120.
[10] Chen, Y. and Shum, K.P., Projective and indecomposable S-acts, Sci. China Ser. A 42 (1999), 593-599.
[11] Fountain, J., Perfect semigroups, Proc. Edinburgh Math. Soc. 20(2) (1976), 87-93.
[12] Freyd, P. and Scedrov, A., "Categories, Allegories", North-Holland Publishing Co., 1990.
[13] Garraway, W.D., Sheaves for an involutive quantaloid, Cah. Topol. Géom. Différ. Catég. 46 (2005), 243-274.
[14] Gumm, H.P., Functors for coalgebras, Conference on Lattices and Universal Algebra (Szeged, 1998), Algebra Universalis 45 (2001), 135-147.
[15] Kilp, M., On flat acts (in Russian), Tartu Riikl. Ül. Toimetised 253 (1970), 66-72.
[16] Kilp, M., Knauer, U., and A.V. Mikhalev, A.V., "Monoids, Acts and Categories", Walter de Gruyter & Co., 2000.
[17] Laan, V., Acceptable Morita contexts for semigroups, ISRN Algebra 2012, Art. ID 725627, 5 pp.
[18] Laan, V., Márki, L., and Reimaa, Ü., Morita equivalence of semigroups revisited: firm semigroups, J. Algebra 505 (2018), 247-270.
[19] Laan, V. and Reimaa, Ü. Morita equivalence of factorizable semigroups, Internat. J. Algebra Comput. 29 (2019), 723-741.
[20] Laan, V. and Reimaa, Ü., Monomorphisms in categories of firm acts, Studia Sci. Math. Hungar. 56 (2019), 267-279.
[21] Lawson, M.V., Morita equivalence of semigroups with local units, J. Pure Appl. Algebra 215 (2011), 455-470.
[22] Mac Lane, S., "Categories for the Working Mathematician", Springer-Verlag, 1998.
[23] Quillen, D., Module theory over nonunital rings, 1996, available at http://www.claymath.org/library/Quillen/Working_papers/quillen%201996/ 1996-2.pdf
[24] Stenström, B., Flatness and localization over monoids, Math. Nachr. 48 (1971), 315-334.