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Sequential Path Objects

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If you have a question about this talk, please contact Sean Moss.

Recall that we have a notion of paths in graphs: these are strings of “composable” edges. Given an internal multigraph (= multiple edges allowed) on an object in a category, we can construct the object of paths in the multigraph, assuming that the category has necessary structures that facilitate the construction like the natural number object.

If the objects of a category come equipped with a “natural” internal multigraph, then the aforementioned construction equips the objects of the category with a “natural” object of paths. This construction conceptualizes the path object of Jaap van Oosten in the effective topos.

My talk will be anecdotes about this “sequential path object” from the viewpoint of modelling intensional type theory.

This talk is part of the Junior Category Theory Seminar series.

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