Algebraic lattices and locally finitely presentable categories (Q539981)

Lattices of subobjects and lattices of quotients are ubiquitous in universal algebra and their basic property is that they are algebraic. The author extends this fact from varieties of universal algebras to locally finitely presentable categories. These categories correspond to varieties of partial algebras where definition domains of partial operations are given by equations in previous operations. This generalization is illustrated by natural examples.