As suggested by Gerald, the notion was first introduced for groups. Given a directed system of groups, their direct limit was defined as a quotient of their direct product (which was referred to as their "weak product"). The general notion is a clear generalization, although the original reference only deals with groups. As mentioned by Cameron Zwarich in the other answer, the definition is due to Lev Pontryagin.

For an early exposition in English, see

MR0007093 (4,84f). Lefschetz, Solomon. Algebraic Topology. American Mathematical Society Colloquium Publications, v. 27. American Mathematical Society, New York, 1942. vi+389 pp.

Specifically, direct limits are defined in Chapter 2, $\S$14 (p. 57).

As suggested by Gerald, the notion was first introduced for groups. Given a directed system of groups, their direct limit was defined as a quotient of their direct product (which was referred to as their "weak product"). The general notion is a clear generalization, although the original reference only deals with groups. As mentioned by Cameron Zwarich in the other answer, the definition can be traced back at least to Lev Pontryagin.

For an early exposition in English, see

MR0007093 (4,84f). Lefschetz, Solomon. Algebraic Topology. American Mathematical Society Colloquium Publications, v. 27. American Mathematical Society, New York, 1942. vi+389 pp.

Specifically, direct limits are defined in Chapter 2, $\S$14 (p. 57).

As suggested by Gerald, the notion was first introduced for groups. Given a directed system of groups, their direct limit was defined as a quotient of their direct product (which was referred to as their "weak product"). The general notion is a clear generalization, although the original reference only deals with groups. See

MR0007093 (4,84f). Lefschetz, Solomon. Algebraic Topology. American Mathematical Society Colloquium Publications, v. 27. American Mathematical Society, New York, 1942. vi+389 pp.

Specifically, direct limits are defined in Chapter 2, $\S$14 (p. 57).

As suggested by Gerald, the notion was first introduced for groups. Given a directed system of groups, their direct limit was defined as a quotient of their direct product (which was referred to as their "weak product"). The general notion is a clear generalization, although the original reference only deals with groups. As mentioned by Cameron Zwarich in the other answer, the definition is due to Lev Pontryagin.

For an early exposition in English, see

MR0007093 (4,84f). Lefschetz, Solomon. Algebraic Topology. American Mathematical Society Colloquium Publications, v. 27. American Mathematical Society, New York, 1942. vi+389 pp.

Specifically, direct limits are defined in Chapter 2, $\S$14 (p. 57).