We describe an equivalent formulation of algebraic weak factorisation systems, not involving monads and comonads, but involving double categories of morphisms equipped with a lifting operation satisfying lifting and factorisation axioms.Comment: Added intro to double categories and discussion of homotopical examples. Journal versio
AbstractIt is shown that many weak factorization systems appearing in functorial Quillen model categ...
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in...
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of...
summary:In order to facilitate a natural choice for morphisms created by the (left or right) lifting...
Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring that the ...
The aim of this note is to briefly summarize techniques for building weak factor-ization systems who...
We investigate the categories of weak maps associated to an algebraic weak factorisation system (awf...
Abstract: This paper introduces lax orthogonal algebraic weak factorisation sys-tems on 2-categories...
This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and descr...
AbstractA functorial notion of factorization system is introduced and shown to coincide with the app...
We show that the homotopy category can be assigned to any category equipped with a weak factorizatio...
We show that the homotopy category can be assigned to any category equipped with a weak factorizatio...
Let $\mathbb{A}$ be a $2$-category with suitable opcomma objects and pushouts. We give a direct proo...
We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$laxly extended to $V$-$\math...
In this article the notions of semi weak orthogonality and semi weak factorization structure in a ca...
AbstractIt is shown that many weak factorization systems appearing in functorial Quillen model categ...
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in...
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of...
summary:In order to facilitate a natural choice for morphisms created by the (left or right) lifting...
Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring that the ...
The aim of this note is to briefly summarize techniques for building weak factor-ization systems who...
We investigate the categories of weak maps associated to an algebraic weak factorisation system (awf...
Abstract: This paper introduces lax orthogonal algebraic weak factorisation sys-tems on 2-categories...
This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and descr...
AbstractA functorial notion of factorization system is introduced and shown to coincide with the app...
We show that the homotopy category can be assigned to any category equipped with a weak factorizatio...
We show that the homotopy category can be assigned to any category equipped with a weak factorizatio...
Let $\mathbb{A}$ be a $2$-category with suitable opcomma objects and pushouts. We give a direct proo...
We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$laxly extended to $V$-$\math...
In this article the notions of semi weak orthogonality and semi weak factorization structure in a ca...
AbstractIt is shown that many weak factorization systems appearing in functorial Quillen model categ...
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in...
In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of...
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