All Questions
Tagged with algebraic-theory monads
7 questions
4
votes
1
answer
208
views
What should be required from a model category so that the category of algebraic objects in it has the natural model structure?
I have two reference questions
What should be required of a category with finite products so that a (multi-sorted, finitary) Lawvere theory induces a monadic adjunction on it? This should be ...
- 30.3k
3
votes
1
answer
205
views
Commuting filtered colimits & finite limits in infinitary theories
Filtered colimits & finite limits commute in categories that are finitary monadic over Set (i.e. algebras of finitary algebraic theories). Results such as Fred Linton's result that if categories ...
- 64k
2
votes
1
answer
214
views
Literature about the category of finitary monads
This answer states that the category of finitary monads is locally presentable and monadic over the category $\mathrm{Set}^{\mathbb{N}}$. Where can I find proof of this claim?
More generally: I've ...
- 10.7k
16
votes
2
answers
2k
views
Why are operads sometimes better than algebraic theories?
Question 1: Are there any contexts in which replacing the category of (non-symmetric or symmetric) operads (in some monoidal category or symmetric monoidal category, respectively) with the category of ...
- 42.4k
6
votes
0
answers
125
views
Original reference for the correspondence between commutative algebraic theories and commutative monads
Commutative algebraic theories were introduced by Linton in the 1966 paper Autonomous Equational Categories. Commutative monads were introduced by Kock in the 1970 paper Monads on symmetric monoidal ...
- 10.7k
15
votes
3
answers
768
views
Reference request for Linton's theorems on equational theories
This is a reference request for the following "well-known" theorems in category theory:
There is an equivalence of categories between finitary monads on $\mathbf{Set}$ and finitary Lawvere ...
- 63.1k
7
votes
1
answer
564
views
Characterisation of essentially algebraic theories as monads
The following correspondence between algebraic theories and monads on $\mathbf{Set}$ is well-known (see, for example, Algebraic Theories: A Categorical Introduction to General Algebra).
The ...
- 10.7k