Weak homomorphisms of coalgebras beyond \(\mathsf{Set}\). (English) Zbl 1305.18003
Summary: We study the notion of weak homomorphisms between coalgebras of different types generalizing thereby that of homomorphisms for similarly typed coalgebras. This helps extend some results known so far in the theory of universal coalgebra over \(\mathsf{Set}\). We find conditions under which coalgebras of a set of types and weak homomorphisms between them form a category. Moreover, we establish an Isomorphism Theorem that extends the so-called First Isomorphism Theorem, showing thereby that this category admits a canonical factorization structure for morphisms
MSC:
| 18A32 | Factorization systems, substructures, quotient structures, congruences, amalgams |
| 18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |
| 18A30 | Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) |
| 08C05 | Categories of algebras |
Keywords:
category; functor; coalgebraically equivalent coalgebras; weak homomorphism; closed strong subobjectReferences:
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