… In this language, we formulate and prove several variants of predictions from the physics …
: we review the notions of factorization categories and functors, as well as factorization spaces …

… We unravel the functor L for E a cartesian closed cocomplete ∞-category in §4, providing
an explicit tangible expression for it — this follows proof strategy of [Yua23, Proposition 5.10]. …

… The category Quiver of finite quivers and morphisms of quivers is the functor category Fun(2,…
Therefore, homological invariants of categories yield the same invariants for quivers; we …

… This homology group can be regarded as a special case of a … the homology of a small category
with coefficients in a functor. … of the homology of small category as a derived functor. In the …

… mod A ) consisting of complexes with the i-th homology is 0 for any i ∉ I . For instance, K { 0 }
… this paper, all functors between triangulated categories are assumed to be triangle functors. …

… a category is unique. Finally, we give a proof for the known fact that any abelian category is
… In case we consider direct limits or inverse limits (colimits or limits of functors from a directed …

… functor through a transfinite composition of monadic functors. More precisely, given a right
adjoint functor G : D → C of (large) ∞-categories, … the subject of homology localizations and …

… basic terminology of relative homological algebra. We also … define the functor Θ by using
idempotent embedding functors in … category of (covariant) functors from P to the category of finite …

… At the state of the art, the most well-behaved link homology theories assign homotopy classes
… Moreover, we say that a functor between (∞, 2)-categories is faithful if it is fully faithful on …

… has finite global dimension (ie, Db sg(R) reflects homological … triangulated category is called
the singularity category of R … triangulated functors from (bounded) n-pure derived categories…