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Using of category theory in computer science has extremely growth in the last decade. Categories allow us to express mathematical structures in unified way. Algebras are used for constructing basic structures used in computer programs. A program can be considered as an element of the initial algebra arising from the used programming language. In our contribution we formulate two ways of expressing algebras in categories. We also construct the codomain functor from the arrow category of algebras into the base category of sets which objects are also the carrier-sets of the algebras. This functor expresses the relation between algebras and carrier-sets.