论文标题
lovàsz的hom-hom-count-theorem通过包容性排斥原则
Lovàsz's hom-counting theorem by inclusion-exclusion principle
论文作者
论文摘要
令$ {\ Mathcal C} $为有限图的类别。 lovàsz（1967）表明，如果$ | \ m atrm {hom}（x，a）| = | = | \ mathrm {hom}（x，b）| $持有任何$ x $，则$ a $ a $是$ b $的同构。 Pultr（1973）使用类似的论点进行了分类概括。两个证据都假设每个对象都有有限数量的子对象的同构类别。没有这种假设的概括由Dawar，Jakl和Reggio（2021）和Regio（2021）给出。在这里，给出了一个没有这个假设的概括，并提供了较短的证明。给出了类别的示例，我们的定理适用，但现有定理不适用。
Let ${\mathcal C}$ be the category of finite graphs. Lovàsz (1967) shows that if $|\mathrm{Hom}(X,A)|=|\mathrm{Hom}(X,B)|$ holds for any $X$, then $A$ is isomorphic to $B$. Pultr (1973) gives a categorical generalization using a similar argument. Both proofs assume that each object has a finite number of isomorphism classes of subobjects. Generalizations without this assumption are given by Dawar, Jakl, and Reggio (2021) and Regio (2021). Here another generalization without this assumption is given, with a shorter proof. Examples of categories are given, for which our theorem is applicable, but the existing theorems are not.
