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Digraph functors which admit both left and right adjoints

Foniok, J and Tardif, C (2014) Digraph functors which admit both left and right adjoints. Discrete Mathematics, 338. ISSN 0012-365X

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Abstract

For our purposes, two functors ΛΛ and ΓΓ are said to be adjoint if for any digraphs GG and HH, there exists a homomorphism of Λ(G)Λ(G) to HH if and only if there exists a homomorphism of GG to Γ(H)Γ(H). We investigate the right adjoints characterised by Pultr (1970). We find necessary conditions for these functors to admit right adjoints themselves. We give many examples where these necessary conditions are satisfied, and the right adjoint indeed exists. Finally, we discuss a connection between these right adjoints and homomorphism dualities.

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