Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Of or pertaining to a functor
Etymologies
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Examples

In what follows, we distinguish three types of account of what it is to be a fact in the functorial sense and consider some possible roles for facts which have been thought to yield arguments in favour of admitting facts into our inventory of what there is.

We may, then, distinguish between Humean facts and functorial facts.

Or one may think that all facts in the functorial sense are contingent, are Humean matters of fact.

The word “fact”, particularly when it is understood in the functorial sense, belongs to a family of related terms:

Moreover, this correspondence is functorial: any Boolean homomorphism is sent to a continuous map of topological spaces, and, conversely, any continuous map between the spaces is sent to a Boolean homomorphism.

The association of MZVs to patterns arising from operads is quite functorial, leading one to suspect that MZVs should be defined not from the point of view of standard analysis, but as canonical numerical invariants for categorical structures.

Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem.

Conal was looking at it more from the functorial point of view, you're starting a bit more directly from models.

One may think that there are facts in the functorial sense of the word which are contingent ” the fact that Sam is sad ” and facts in the functorial sense which are not contingent ” the fact that 2 + 2 =
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