Unitalities and mapping spaces in $A_\infty$-categories

TL;DR

This paper establishes an equivalence between strictly unital and unital A-infinity-categories over any base ring, and characterizes models for internal homs and mapping spaces in related infinity-categories.

Contribution

It proves the equivalence of strictly unital and unital A-infinity-categories over any base ring and identifies models for internal homs and mapping spaces in dg- and A-infinity-categories.

Findings

Equivalence of strictly unital and unital A-infinity-categories over any base ring

Identification of models for internal homs in dg- and A-infinity-categories

Generalization of results by Toën and Faonte

Abstract

We prove, over any base ring, that the infinity-category of strictly unital A-infinity-categories (and strictly unital functors) is equivalent to the infinity-category of unital A-infinity-categories (and unital functors). We also identify various models for internal homs and mapping spaces in the infinity-categories of dg-categories and of A-infinity--categories, generalizing results of To\"en and Faonte.