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### Is there a nice formula for the “non-crossing substitution” of linear combinatorial species?

Background A linear species is a functor $$F : \mathrm{Lin} \to \mathrm{FinSet},$$ where $\mathrm{Lin}$ is the category of totally ordered sets and bijections and $\mathrm{FinSet}$ is the category ...
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### Anti-arithmetic product of symmetric functions: (why) is it integral?

This is an analogue of MathOverflow question #138148. Indeed it is so analogous that I wrote the following by copypasting said question and making the necessary changes. For every commutative ring $A$...
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### Arithmetic product of symmetric functions: why is it integral?

For every commutative ring $A$, let $\mathbf{Symm}_A$ be the ring of symmetric functions over $A$. Let $\mathbf{Symm}$ without a subscript denote $\mathbf{Symm}_{\mathbb{Z}}$. We can define a ...
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### On the category of virtual species

In Foncteurs analytiques et espèces de structures, Joyal defines virtual species, as a (quotient) of formal differences of functors $F,G:\mathbb{B}\rightarrow \mathsf{Set}$, and then proceeds to show ...