기초과학연구원 이산수학그룹
On April 23, 2024, Víctor Dalmau from the Universitat Pompeu Fabra in Barcelona gave a talk at the Discrete Math Seminar on the right adjoints of Datalog Programs. The title of his talk was “Right-adjoints of Datalog Programs“.
We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ(A) maps homomorphically to B if and only if A maps homomorphically to Γ(B). If this is the case Λ is called the left adjoint to Γ and Γ the right adjoint to Λ. In 2015, Foniok and Tardif described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We shall present several recent advances in this direction including a new approach based on the notion of Datalog Program borrowed from logic.